*This article focuses on the robust reliable dissipative control issue for a class of switched discrete-time nonlinear networked control systems with external energy bounded disturbances. In particular, nonlinearities are modeled in a probabilistic way according to Bernoulli distributed white sequence with known conditional probability. A Lyapunov–Krasovskii functional is proposed based on which sufficient conditions for the existence of the reliable dissipative controller are derived in terms of linear matrix inequalities (LMIs) which ensures exponentially stability as well as*
*dissipative performance of the resulting closed-loop system. The explicit expression of the desired controller gains can be obtained by solving the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed design strategy*. © 2016 Wiley Periodicals, Inc. Complexity, 2016

This article deals with the problem of synchronization of fractional-order memristor-based BAM neural networks (FMBNNs) with time-delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional-order 0 < *α* < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master-slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite-time synchronization of FMBNNs with fractional-order 1 < *α* < 2, using Mittag-Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time-delay and fractional-order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity, 2016

A definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science was explored. Detailed numerical analysis shows that (i) logic complexity is effective in discriminating between classes of functions commonly employed in modeling contexts; (ii) it extends the notion of canalization, used in the study of genetic regulation, to a more general and detailed measure; (iii) it is tightly linked to the resilience of a function's output to noise affecting its inputs. Its utility was demonstrated by measuring it in empirical data on gene regulation. Logic complexity is exceptionally low in these systems, and the asymmetry between “on” and “off” states in the data correlates with the complexity in a non-null way. A model of random Boolean networks clarifies this trend and indicates a common hierarchical architecture in the three systems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>An H-system is a conceptual or semiotic model of reality formed in the mind of the subject. Understanding the behavior of the system means being able to infer causal relationships that explain this system to the Observer-subject, and therefore having access to mechanisms to construct a mental or ontological mathematical model of the system under study. A process is a mechanism involving a series of successive operations between stimuli and responses. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, the problem of cluster synchronization in the complex networks with nonidentical nonlinear dynamics is considered. By Lyapunov functional and *M*-matrix theory, some sufficient conditions for cluster synchronization are obtained. Moreover, the least number of nodes which should be pinned is given. It is shown that when the root nodes of all the clusters are pinning-controlled, cluster synchronization with adaptive coupling strength can be achieved. Different from the constraints of many literatures, the assumption is that each row sum for all diagonal submatrices of the Laplacian matrix is equal to zero. Finally, a numerical simulation in the network with three scale-free subnetwork is provided to demonstrate the effectiveness of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity, 2016

In this article, the finite-time stochastic stability of fractional-order singular systems with time delay and white noise is investigated. First the existence and uniqueness of solution for the considered system is derived using the basic fractional calculus theory. Then based on the Gronwall's approach and stochastic analysis technique, the sufficient condition for the finite-time stability criterion is developed. Finally, a numerical example is presented to verify the obtained theory. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low-dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low-dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>An abrupt transition from sinus rhythm to atrial fibrillation (AF) is common in patients with chronic heart failure (CHF). We propose a conceptual framework for viewing this malignant transition in terms of a type of sublimation marked by the switch from highly periodic sinus interbeat interval dynamics characteristic of CHF to a state of random disorganization with AF. Sublimation of physical substances involves an increase in entropy via heat transfer. In contrast, the disease-related sublimation-like behavior involves a loss of information content, associated decreases in cardiac bioenergetic capacity and in multiscale entropy. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The syntactic structure of sentences exhibits a striking regularity: dependencies tend to not cross when drawn above the sentence. We investigate two competing explanations. The traditional hypothesis is that this trend arises from an independent principle of syntax that reduces crossings practically to zero. An alternative to this view is the hypothesis that crossings are a side effect of dependency lengths, that is, sentences with shorter dependency lengths should tend to have fewer crossings. We are able to reject the traditional view in the majority of languages considered. The alternative hypothesis can lead to a more parsimonious theory of language. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article examines the reliable L_{2} – L_{∞} control design problem for a class of continuous-time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled-data controller that guarantees the robust asymptotic stability of the resulting closed-loop system with an L_{2} – L_{∞} prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled-data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity, 2016

Integration of renewable generations, such as wind and photovoltaic, into electrical power systems is rapidly growing throughout the world. Stochastic and variable nature of these resources makes some operational challenges to power systems. The most effective way to tackle these challenges is short-term prediction of their available powers. Despite various developed methods to forecast generation of renewable resources, still they have large errors, which may lead to under/over-commitment of conventional generators in power systems. Prediction of net demand (ND), defined as electrical load minus renewable generations, can provide useful information for accurate scheduling of conventional generators. In this article, characteristics of the time series of electric load, renewable generations and ND are analyzed, and a new hybrid prediction strategy is presented for direct prediction of ND. The training mechanism of the proposed forecasting engine is composed of a new stochastic search method and Levenberg–Marquardt learning algorithm based on an iterative procedure and greedy search. The suggested prediction strategy is tested on different real-world power systems and its obtained results are compared with the results of several other forecast methods and published literature figures. These comparisons confirm the validity of the developed forecasting strategy. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This study aimed to verify the network of interactions resulting from the collective behavior of professional football teams and the influence of ball possession. A dataset of 30 matches of one highly successful team from the Portuguese Premier League, season 2010/2011, was considered. From these 30 matches, 13,958 passes (e.g., 11,127 successfully passes and 2831 unsuccessfully passes) and 7583 collective offensive actions were analysed. The data were analysed using Node XL Template that allows to characterize networks and team activity profiles. The results showed that football players' interactions tended to occur, preferentially, during the offensive phase, wherein the network of contacts was mainly organised in the central and lateral areas of the field. We concluded that the ball possession during a football match endows the team with a larger domain in terms of game actions. Moreover, the results of this study also allow concluding that the ball possession does not significantly influence the final outcome of the game. This study has practical implications for coaches, since it provides a multidimensional analysis of the football match (e.g., networks and ball possession) and offers relevant insights on how creative and organizing individuals might act to orchestrate team strategies. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In finance, the asymmetric volatility phenomenon (AVP) and volatility skew are two well-known topics related to firm risk. In early research, the AVP was documented by Black (Proc 1976 Meetings Business Econ Stat Sect 1976, 177–181), who proposed two possible explanations. The veracity of one such explanation, the “leverage effect,” has long remained controversial. The volatility skew is considered to represent collective phenomena caused by heterogeneous beliefs regarding firm risk among investors. Although the relationship between leverage and firm size has been investigated, the investigations have yielded inconsistent conclusions. All related empirical evidence indicates that the relationships among firm risk, asymmetric volatility, volatility skew, and the leverage effect are complex. Regarding accounting principles, Ryan (Account Horizons 1997, 11, 85–95) proposed two concepts for describing firm risk. One of those concepts, “sources of operating risk versus leverage,” revealed the key to linking firm risk to leverage. Among the multidisciplinary methodologies, cybernetics plays a crucial role in complex systems research. The causal nets and feedback loop analysis of cybernetics offer accurate descriptions of realities in terms of causality, nonlinearity, and temporality. This study uses cybernetics to connect the accounting risk concept in microlevel analysis to volatility changes in macrolevel phenomena. This not only validates interdisciplinary analysis with different evidence but also enables the development of a managerial interpretation of different states of firm risk. This study contributes a novel approach that involves the application of a microlevel concept to macrolevel analysis and evidences the “less is more” art of modeling complex phenomena (Schuster, Complexity 2005, 11, 11–13). © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The important issue of reducing the conservatism of feasible stability criteria for continuous-time Takagi–Sugeno fuzzy systems is studied in this article. In order to obtain more advanced result than previous ones, a new upper bound inequality is proposed and thus the properties of the normalized fuzzy weighting functions' time derivatives can be better used than the previous ones. In particular, the so-called “redundant terms” considered in previous literature can be converted to “useful terms” which play a positive role in the underlying analysis process. Moreover, some useless additional variables and their derived inequalities are removed for enhancing the efficiency. Finally, an illustrative example is given to show the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article addresses the decentralized output feedback control for discrete-time large-scale nonlinear systems. The considered large-scale system contains several subsystems with nonlinear interconnection and time-varying delay, and Takagi–Sugeno model is used to represent each nonlinear subsystem. We aim at designing a decentralized piecewise fuzzy memory dynamic-output-feedback (DOF) controller that guarantees the stabilization and performance of the resulting closed-loop control system. First, we propose a model transformation that reformulates the problem of decentralized output feedback control into the stability analysis with input–output form. Then, we introduce a piecewise Lyapunov–Krasovskii functional, where all Lyapunov matrices are not necessarily positive definite. By combining with the scaled small gain theorem, the less conservative solution to the problem of decentralized piecewise fuzzy memory DOF controller design for the considered system is derived in terms of linear matrix inequalities. The advantage of the proposed method is finally validated using two numerical examples. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The process of learning scientific knowledge from the dynamic systems viewpoint is studied in terms probabilistic learning model (PLM), where learning accrues from foraging in the epistemic landscape. The PLM leads to the formation of attractor-type regions of preferred models in an epistemic landscape. The attractor-type states correspond to robust learning outcomes which are more probable than others. These can be assigned either to the high confidence in model selection or to the dynamic evolution of a learner's proficiency, which depends on the learning history. The results suggest that robust learning states are essentially context dependent, and that learning is a continuous development between these context dependent states. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The combustion temperature and progress control problems are key factors to ensure the production quality of metallurgy lime kiln. The combustion process of lime kiln is a nonlinear and large time-delay thermal process, so it is difficult to achieve satisfactory results by the traditional proportional integral derivative control, fuzzy control, or predictive control. This article analyses physics and chemistry mechanism of the combustion process and expounds the complex nonlinear, multivariable and large time-delay characteristics, and the control target of the production system. Then, the mathematical model of combustion control system is deduced in view of the requirements of simulation. Based on these, the fuzzy predictive control scheme is employed. Through simulation, the control algorithm is verified to be effective. Finally, the industrial sleeve kiln as a practical example is used to demonstrate the effectiveness and feasibility of the control algorithm. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Cartography is the art of map-making that integrates science, technology, and visual aesthetics for the purpose of rendering the domain of interest, navigable. The science could aid the cartographer if it were to inform about the underlying process. Thus, Mendeleev's periodic table was informed by insights about the atomic mass periodicity. Likewise, Harvey's work on the circulatory system map was informed by his theoretical insights on Galen's errors. Mapping of human knowledge dates back at least to Porphyry who laid out the first tree-of-knowledge. Modern knowledge-cartographers use a wide array of scientometric techniques capable of rendering appealing visuals of massive scientific corpuses. But what has perhaps been lacking is a sound theoretical basis for rendering legible the adaptive dynamics of knowledge creation and accumulation. Proposed is a theoretical framework, knowledge as a complex adaptive system (CAS) patterned on Holland's work on CAS, as well as the view that knowledge is a hierarchically heterarchic dynamical system. As a first leg in the conjoining experimental phase, we extract terms from approximately 1400 complexity science papers published at the Santa Fe Institute, deduce the topic distribution using Latent Dirichlet Allocation, capture the underlying dynamics, and show how to navigate the corpus visually. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Light switching games are both popular and well studied. This article introduces a cellular automaton called Langton's turmite to several different light switching scenarios and discusses when Langton's turmite can solve these games. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, some dynamics of Bloch chaotic system have been studied. Based on Lagrange multiplier method, optimization theory, and the generalized positively definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and a family of mathematical expressions of globally exponentially attractive sets for this system with respect to the parameters of system. The results obtained in this article provides theory basis for chaotic synchronization, chaotic control, Hausdorff dimension, and Lyapunov dimension of chaotic attractors of Bloch chaotic system. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Synergy is often defined as the creation of a whole that is greater than the sum of its parts. It is found at all levels of organization in physics, chemistry, biology, social sciences, and the arts. Synergy occurs in open irreversible thermodynamic systems making it difficult to quantify. Negative entropy or negentropy ( ) has been related to order and complexity, and so has work efficiency, information content, Gibbs Free Energy in equilibrium thermodynamics, and useful work efficiency in general ( ). To define synergy in thermodynamic terms, we use the quantitative estimates of changes in and in seven different systems that suffer process described as synergistic. The results show that synergistic processes are characterized by an increase in coupled to an increase in . Processes not associated to synergy show a different pattern. The opposite of synergy are dissipative processes such as combustion where both and decrease. The synergistic processes studied showed a relatively greater increase in compared to opening ways to quantify energy—or information—dissipation due to the second law of thermodynamics in open irreversible systems. As a result, we propose a precise thermodynamic definition of synergy and show the potential of thermodynamic measurements in identifying, classifying and analysing in detail synergistic processes. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, we consider a mini-max multi-agent optimization problem where multiple agents cooperatively optimize a sum of local convex–concave functions, each of which is available to one specific agent in a network. To solve the problem, we propose a distributed optimization method by extending classical mirror descent algorithms to the distributed setting. We obtain the convergence of the algorithm under wild conditions that the agent communication follows a directed graph and the related weighted matrices are row stochastic. In particular, when the weighted matrices are restricted to be doubly stochastic, we provide the explicit convergence rate of the algorithm by choosing the stepsize in a suitable way. The proposed algorithm can be viewed as a generalization of the subgradient projection methods since it utilizes a customized Bregman divergence instead of the usual Euclidean squared distance. Finally, some simulation results on a matrix game are presented to illustrate the performance of the algorithm. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article deals with the positioning control problem via the output feedback scheme for a linear actuator with nonlinear disturbances. In this study, the proposed controller accounts for not only the nonlinear friction, force ripple, and external disturbance but also the input saturation problem. In detail, the energy consumption for conquering friction and disturbance rejection is estimated and used as compensation based on the hybrid controller including and sliding-mode-based adaptive algorithms, which ensures the tracking performance and robustness of electromechanical servo system. Moreover, to confront the input saturation, a saturation observer and an anti-windup controller are designed. The global robustness of the controller is guaranteed by an output feedback robust law. Theoretically, the designed controller can guarantee a favorable tracking performance in the presence of various disturbance forces and input saturation, which is essential for high accuracy motion plant in industrial application. The simulation results verify the robustness and effectiveness for the motion system with the proposed control strategy under various operation conditions. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article is devoted to designing linear sliding surface and adaptive sliding mode controller for a class of singular time-delay systems with parametric uncertainties and external disturbance. In terms of linear matrix inequalities (LMIs), a sufficient criteria of **H _{∞}** performance, and admissibility for considered sliding motion restricted to linear sliding surface is achieved, and the controller which guarantees the finite-time reachability of the predesigned sliding surface is then developed, respectively. Finally, three examples show the effectiveness of the proposed result. © 2016 Wiley Periodicals, Inc. Complexity, 2016

We analyze the global pharmaceutical industry network using a unique database that covers strategic transactions (i.e., alliance, financing and acquisition collaborations) for the top 90 global pharmaceutical firms and their ego-network partnerships totaling 4735 members during 1991–2012. The article explores insights on dynamic embeddedness analysis under network perturbations by exploring core and full networks' behavior during the global financial crisis of 2007–2008 and the subsequent global and Eurozone recessions of 2009–2012. We introduce and test literature grounded hypotheses as well as report network visualizations and nonparametric tests that reveal important discrepancies in both network types before and after the financial crisis offset. We observe that firms in core and full networks behave differently, with smaller top pharmaceutical firms of core networks particularly being affected by the crises, potentially due to a collaboration reduction with bigger top pharmaceuticals. On the other hand, big pharmaceuticals in full networks maintain their centrality position as a possible consequence of their strategic collaborations not only with other similarly sized firms but also due to their connections with subsidiaries and other private entities present in the total sample. Our results confirm the significant dynamicity reduction during financial crisis and recession periods for core and full networks, and highlight the importance that exogenous factors as well as network types play in centrality-based dynamic longitudinal network analysis. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Intuitionistic fuzzy set plays a vital role in decision making, data analysis, and artificial intelligence. Many decision-making problems consist of different types of datum, where fuzzy set theoretical approaches may fail to obtain the optimal decision. Numerous approaches for intuitionistic fuzzy decision-making problem have been introduced in the literature to overcome these short comings. But there is no single approach that can be used to solve all kinds of problems because of the partial ordering defined on the collection of intuitionistic fuzzy numbers (IFNs). Even though ranking of fuzzy numbers have been studied from early seventies in the last century, a total order on the entire class of fuzzy numbers has been introduced by Wang and Wang (*Fuzzy Sets Syst* 2014, 243, 131–141) only on 2014. A total order on the collection of all IFN is an open problem till today. In this article, a total order on the entire class of IFN using upper lower dense sequence in the interval [0, 1] is proposed and compared with existing techniques using illustrative examples, further an algorithm (which is problem independent) for solving any intuitionistic fuzzy multicriteria decision-making problem (Intuitionistic fuzzy MCDM) is introduced. This new total ordering on IFNs generalizes the total ordering defined in Wang and Wang () for fuzzy numbers. © 2016 Wiley Periodicals, Inc. Complexity, 2016

Short-Term Price Forecast is a key issue for operation of both regulated power systems and electricity markets. Energy price forecast is the key information for generating companies to prepare their bids in the electricity markets. However, this forecasting problem is complex due to nonlinear, nonstationary, and time variant behavior of electricity price time series. So, in this article, the forecast model includes wavelet transform, autoregressive integrated moving average, and radial basis function neural networks (RBFN) is presented. Also, an intelligent algorithm is applied to optimize the RBFN structure, which adapts it to the specified training set, reduce computational complexity and avoids over fitting. Effectiveness of the proposed method is applied for price forecasting of electricity market of mainland Spain and its results are compared with the results of several other price forecast methods. These comparisons confirm the validity of the developed approach. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article presents the general case-study of our previous works regarding generalized Boussinesq equations [17, 18, 19], that focus on application of various subordinate methods where are applied to construct more general exact solutions of the coupled Boussinesq equations. In this article, the -expansion method is applied on coupled Boussinesq equations. Our work is motivated by the fact that the -expansion method provides not only more general forms of solutions but also periodic, solitary waves, and rational solutions. The method appears to be easier and faster by means of a symbolic manipulation program. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this paper, the consensus problem of uncertain nonlinear multi-agent systems is investigated via reliable control in the presence of probabilistic time-varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time-varying delay is equivalently transformed into the deterministic time-varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed-loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly stable in the sense of mean-square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay-dependent consensus stabilizability conditions for the closed-loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, a partially delay-dependent controller is designed to analyze the guaranteed performance analysis of a class of uncertain discrete-time systems with time-varying delays. By constructing suitable Lyapunov–Krasovskii Functional (LKF), sufficient conditions are derived to ensure the system to be robustly stochastically stable in mean square sense by using Wirtinger-based inequality and convex reciprocal lemma. The proper cost function is chosen to guarantee an adequate level of performance. The derived conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in MATLAB. Further, the advantage of employing the obtained results is illustrated via numerical examples. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer-to-peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real-world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game-theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer-to-peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer-to-peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Probability distributions have proven effective at modeling diversity in complex systems. The two most common are the Gaussian normal and skewed-right. While the mechanics of the former are well-known; the latter less so, given the significant limitations of the power-law. Moving past the power-law, we demonstrate that there exists, hidden-in-full-view, a limiting law governing the diversity of complexity in skewed-right systems; which can be measured using a case-based version of Shannon entropy, resulting in a 60/40 rule. For our study, given the wide range of approaches to measuring complexity (i.e., descriptive, constructive, etc), we examined eight different systems, which varied significantly in scale and composition (from galaxies to genes). We found that skewed-right complex systems obey the law of restricted diversity; that is, when plotted for a variety of natural and human-made systems, as the diversity of complexity (primarily in terms of the number of types; but also, secondarily, in terms of the frequency of cases) a limiting law of restricted diversity emerges, constraining the majority of cases to simpler types. Even more compelling, this limiting law obeys a scale-free 60/40 rule: when measured using , 60%(or more) of the cases in these systems reside within the first 40% (or less) of the lower bound of equiprobable diversity types—with or without long-tail and whether or not the distribution fits a power-law. Furthermore, as an extension of the Pareto Principle, this lower bound accounts for only a small percentage of the total diversity; that is, while the top 20% of cases constitute a sizable percentage of the total diversity in a system, the bottom 60% are highly constrained. In short, as the central limit theorem governs the diversity of complexity in normal distributions, restricted diversity seems to govern the diversity of complexity in skewed-right distributions. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Advances in science are being sought in newly available opportunities to collect massive quantities of data about complex systems. While key advances are being made in detailed mapping of systems, how to relate these data to solving many of the challenges facing humanity is unclear. The questions we often wish to address require identifying the impact of interventions on the system and that impact is not apparent in the detailed data that is available. Here, we review key concepts and motivate a general framework for building larger scale views of complex systems and for characterizing the importance of information in physical, biological, and social systems. We provide examples of its application to evolutionary biology with relevance to ecology, biodiversity, pandemics, and human lifespan, and in the context of social systems with relevance to ethnic violence, global food prices, and stock market panic. Framing scientific inquiry as an effort to determine what is important and unimportant is a means for advancing our understanding and addressing many practical concerns, such as economic development or treating disease. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, the bounds of the Lorenz-like chaotic system describing the flow between two concentric rotating spheres have been studied. Based on Lagrange multiplier method, the function extremum theory and the generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and the globally exponentially attractive set for this system. The results that obtained in this article provides theory basis for chaotic synchronization, chaotic control, Hausdorff dimension and the Lyapunov dimension of chaotic attractors. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, we study the problem of robust H_{∞} performance analysis for a class of uncertain Markovian jump systems with mixed overlapping delays. Our aim is to present a new delay-dependent approach such that the resulting closed-loop system is stochastically stable and satisfies a prescribed H_{∞} performance level χ. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing new Lyapunov-Krasovskii functionals, some novel sufficient conditions are derived to guarantee the stochastic stability of the equilibrium point in the mean-square. Numerical examples show that the obtained results in this article is less conservative and more effective. The results are also compared with the existing results to show its conservativeness. © 2016 Wiley Periodicals, Inc. Complexity, 2016

The reaction-diffusion neural network is often described by semilinear diffusion partial differential equation (PDE). This article focuses on the asymptotical synchronization and synchronization for coupled reaction-diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. First, using the Lyapunov–Krasoviskii functional scheme, the sufficient condition is obtained for the asymptotical synchronization of coupled semilinear diffusion PDEs with mixed time-delays and this condition is represented by linear matrix inequalities (LMIs), which is easy to be solved. Then the robust synchronization is considered in temporal-spatial domain for the coupled semilinear diffusion PDEs with mixed delays and external disturbances. In terms of the technique of completing squares, the sufficient condition is obtained for the robust synchronization. Finally, a numerical example of coupled semilinear diffusion PDEs with mixed time-delays is given to illustrate the correctness of the obtained results. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>An improved nonsingular terminal sliding mode method is proposed for a class of nonlinear systems with unmodeled dynamics. The proposed method can effectively avoid the singularity problem. The stability of the proposed procedure which could guarantee the robustness against uncertain unmodeled dynamic and external disturbances is proven by using the Lyapunov theory in finite time. An example is given to show the proposed improved terminal sliding mode control law without singular effectively. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this work, we are motivated by the observation that previous considerations of appropriate complexity measures have not directly addressed the fundamental issue that the complexity of any particular matter or thing has a significant subjective component in which the degree of complexity depends on available frames of reference. Any attempt to remove subjectivity from a suitable measure therefore fails to address a very significant aspect of complexity. Conversely, there has been justifiable apprehension toward purely subjective complexity measures, simply because they are not verifiable if the frame of reference being applied is in itself both complex and subjective. We address this issue by introducing the concept of subjective simplicity—although a justifiable and verifiable value of subjective complexity may be difficult to assign directly, it is possible to identify in a given context what is “simple” and, from that reference, determine subjective complexity as distance from simple. We then propose a generalized complexity measure that is applicable to any domain, and provide some examples of how the framework can be applied to engineered systems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The article argues that crises are a distinctive feature of complex social systems. A quest for connectivity of communication leads to increase systems' own robustness by constantly producing further connections. When some of these connections have been successful in recent operations, the system tends to reproduce the emergent pattern, thereby engaging in a non-reflexive, repetitive escalation of more of the same communication. This compulsive growth of systemic communication in crisis processes, or logic of excess, resembles the dynamic of self-organized criticality. Accordingly, we first construct the conceptual foundations of our approach. Second, we present three core assumptions related to the generative mechanism of social crises, their temporal transitions (incubation, contagion, restructuring), and the suitable modeling techniques to represent them. Third, we illustrate the conceptual approach with a percolation model of the crisis in Chilean education system. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one-dimensional models exhibit a phase transition at a critical value . We report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This work develops the development of observer-based output feedback control design of discrete-time nonlinear systems in the form of Takagi–Sugeno fuzzy model. Lately, previous results have been improved in virtue of a two-step method. From a technical point of view, it is not flawless and related problems have not been completely resolved. In this study, more advanced two-steps approach is further developed while the relative sizes among different normalized fuzzy weighting functions are utilized by introducing some additional matrix variables. As a result of the above work, those main defects of the existing method can be redressed and a desired solution in aspect of not only reducing the conservatism but also alleviating the computation complexity is provided for some special cases. Moreover, the effectiveness of the proposed result is shown at length by means of an illustrative example. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Natural language is a complex adaptive system with multiple levels. The hierarchical structure may have much to do with the complexity of language. Dependency Distance has been invoked to explain various linguistic patterns regarding syntactic complexity. However, little attention has been paid to how the structural properties of language to minimize dependency distance. This article computationally simulates several chunked artificial languages, and shows, through comparison with Mandarin Chinese, that chunking may significantly reduce mean dependency distance of linear sequences. These results suggest that language may have evolved the mechanism of dynamic chunking to reduce the complexity for the sake of efficient communication. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>“Quorum response” is a type of social interaction in which an individual's chance of choosing an option is a nonlinear function of the number of other individuals already committing to it. This interaction has been widely used to characterize collective decision-making in animal groups. Here, we first implement it in 1D and 2D models of collective animal movement, and find that the resulting group motion shows the characteristic behaviors which were observed in previous experimental and modeling studies. Further, the analytic form of quorum response renders us an opportunity to propose a mean field theory in 1D with globally interacting particles, so we can estimate the average time period between changes in the group direction (mean switching time). We find that the theoretical results provide an upper bound to the simulation results when the interaction radius grows from local to global. Information entropy, a concept widely used to quantify the uncertainty of a random variable, is introduced here as a new order parameter to study the evolution of systems of two cases in 2D models. The explicitly formulated probability of a particle's dynamic state in the framework of quorum response makes information entropy directly computable. We find that, besides the global order, information entropy can also capture the structural features of local order of the system which previous order parameters such as alignment cannot. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This study deals with the pinning synchronization problem for complex dynamical networks (CDNs) with Markovian jumping parameters and mixed delays under sampled-data control technique. The mixed delays cover both discrete and distributed delays. The Markovian jumping parameters are modeled as a continuous-time, finite-state Markov chain. The sufficient conditions for asymptotic synchronization of considered networks are obtained by utilizing novel Lyapunov-Krasovskii functional and multiple integral approach. The obtained criteria is formulated in terms of LMIs, which can be checked for feasibility by making use of available softwares. Lastly, numerical simulation results are presented to validate the advantage of the propound theoretical results. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article addresses the adaptive control of chaotic systems with unknown parameters, model uncertainties, and external disturbance. We first investigate the control of a class of chaotic systems and then discuss the control of general chaotic systems. Based on the backstepping-like procedure, some novel criteria are proposed via adaptive control scheme. As an example to illustrate the application of the proposed method, the control and synchronization of the modified Chua's chaotic system is also investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Electricity load forecasting has become one of the most functioning tools in energy efficiency and load management and utility companies which has been made very complex due to deregulation. Due to the importance of providing a secure and economic electricty for the consumers, having a reliable and robust enough forecast engine in short-term load management is very needful. Fuzzy inference system is one of primal branches of Artificial Intelligence techniques which has been widely used for different applications of decision making in complex systems. This paper aims to develop a Fuzzy inference system as a main forecast engine for Short term Load Forecasting (STLF) of a city in Iran. However, the optimization of this platform for this special case remains a basic problem. Hence, to address this issue, the Radial Movement Optimization (RMO) technique is proposed to optimize the whole Fuzzy platform. To support this idea, the accuracy of the proposed model is analyzed using MAPE index and an average error of 1.38% is obtained for the forecast load demand which represents the reliability of the proposed method. Finally, results achieved by this method, demonstrate that an adaptive two-stage hybrid system consisting of Fuzzy & RMO can be an accurate and robust enough choice for STLF problems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>The stabilizability problem of an unstable non-minimum phase (NMP) plant, controlled over a signal-to-noise ratio (SNR) constrained channel with transmission delay, is investigated in this article. A dynamical output feedback controller is used to stabilize the single-input single-output plant where the control data are exchanged via an NMP bandwidth-limited communication medium. For the first time, a novel description of SNR is used to solve stabilizability problem when the NMP channel imposes a constant delay on transmitted data. It is demonstrated that the presence of time-delay in the channel model as well as its NMP zeros increases the value of SNR needed for stabilizability of the closed-loop system. The main results are illustrated and discussed through numerical examples. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, we propose an endogenous network model for banking systems. Starting from the balance sheets of a banking system and its update algorithms, the interbank credit lending was established based on the partner selection mechanism. Through simulation analysis, we find that the endogenous network model displays a structure with multiple liquidity centers, that the in-degree distribution exhibits a Pareto tail, and that the bank asset distribution is a lognormal distribution with a Pareto tail. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This paper studies the projective synchronization behavior in a drive-response dynamical network with coupling time-varying delay via intermittent impulsive control. Different from the most publications on drive-response dynamical networks under the general impulsive control, here the impulsive effects can only exist at control windows, not during the whole time. Moreover, intermittent impulsive control does not need the limitation of the upper bound of the impulsive intervals. By utilizing the Lyapunov-Razumikhin technique, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Node attributes play an important role in shaping network structures, but are generally ignored in transformations of structural balance. A fully signed network consisting of signs of edges and nodes expresses both properties of relationship and node attributes. In this article, we generalize the definition of structural balance in fully signed networks. We transform the unbalanced fully signed network by not only changing signs of edges but also changing the signs of nodes. We propose a memetic algorithm to transform unbalanced networks at the lowest cost. Experiments show that our algorithm can solve this problem efficiently, and different node attribute assignments may lead to different optimized structures. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article investigates the problem of H_{∞} deconvolution filtering for a kind of uncertain descriptor hybrid system with state time-varying delays, limited communication capacity, and partially unknown transition rates. The limited communication capacity including signal transmission delays and data packet dropout. Mode-dependent and delay-dependent conditions are obtained by constructing a comprehensive stochastic Lyapunov–Krasovskii functional, which ensure the filtering error system is not only stochastically admissible but also satisfies a prescribed H_{∞}-norm level for all admissible uncertainties, signal transmission delays, and data packet dropout. The linear matrix inequalities technique is utilized to acquire the desired deconvolution filter parameters. An electrical RLC circuit example and two numerical examples are provided to demonstrate the usefulness and effectiveness of our methods. © 2016 Wiley Periodicals, Inc. Complexity, 2016

In this article, we investigate the effect of prey refuge and time delay on a diffusive predator-prey system with Holling II functional response and hyperbolic mortality subject to Neumann boundary condition. More precisely, we study Turing instability of positive equilibrium by using refuge as parameter, instability and Hopf bifurcation induced by time delay. In addition, by the theory of normal form and center manifold, we derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This paper presents the authors' responses to comments on their paper “Cracks in the scientific enterprise” which appears in this issue of Complexity. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article deals with the ultimate bound on the trajectories of the hyperchaos Lorenz system based on Lyapunov stability theory. The innovation of this article lies in that the method of constructing Lyapunov functions applied to the former chaotic systems is not applicable to this hyperchaos system, and moreover, one Lyapunov function can not estimate the bounds of this hyperchaos Lorenz system. We successfully estimate the bounds of this hyperchaos system by constructing three generalized Lyapunov functions step by step. Some computer simulations are also given to show the effectiveness of the proposed scheme. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>An algorithm of generating graph structures for the ordering of datasets is proposed. It operates with the key concept of “sphere neighborhood” and generates the graph structured ordering of datasets, provided the elements of such sets can be related by some similarity relation. The algorithm always allows determining the shortest path between two nodes in a constructive way. It is demonstrated by an application to the famous Word Morph game and in addition to the ordering of logfiles with respect to the detection of errors. Therefore, the algorithm can be very useful for the dealing with Big Data problems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article investigates the optimal synchronization of two different fractional-order chaotic systems with two kinds of cost function. We use calculus of variations for minimizing cost function subject to synchronization error dynamics. We introduce optimal control problem to solve fractional Euler–Lagrange equations. Optimal control signal and minimum time of synchronization are obtained by proposed method. Examples show the optimal synchronization of two different systems with two different cost functions. First, we use an ordinary integer cost function then we use a fractional-order cost function and comparing the results. Finally, we suggest a cost function which has the optimal solution of this problem, and we can extend this solution to solve other synchronization problems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>An optimal control scheme is proposed to stabilize complex networks in finite time. Furthermore, since it is costly and impractical to control a network by applying controllers to all the nodes, an algorithm inspired by Kalmans controllability rank condition is presented for local stabilization by locating pinned components. Numerical examples are provided to illustrate the effectiveness of the proposed method as well as its superiority over a traditional pinning control technique. This work offers a theoretical framework for designing optimal controllers to stabilize networks in finite time with reduced control cost. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>This article investigates the stabilization and control problems for a general active fault-tolerant control system (AFTCS) in a stochastic framework. The novelty of the research lies in utilizing uncertain nonhomogeneous Markovian structures to take account for the imperfect fault detection and diagnosis (FDD) algorithms of the AFTCS. The underlying AFTCS is supposed to be modeled by two random processes of Markov type; one characterizing the system fault process and the other describing the FDD process. It is assumed that the FDD algorithm is imperfect and provides inaccurate Markovian parameters for the FDD process. Specifically, it provides uncertain transition rates (TRs); the TRs that lie in an interval without any particular structures. This framework is more consistent with real-world applications to accommodate different types of faults. It is more general than the previously developed AFTCSs because of eliminating the need for an accurate estimation of the fault process. To solve the stabilizability and the controller design problems of this AFTCS, the whole system is viewed as an uncertain nonhomogeneous Markovian jump linear system (NHMJLS) with time-varying and uncertain specifications. Based on the multiple and stochastic Lyapunov function for the NHMJLS, first a sufficient condition is obtained to analyze the system stabilizability and then, the controller gains are synthesized. Unlike the previous fault-tolerant controllers, the proposed robust controller only needs to access the FDD process, besides it is easily obtainable through the existing optimization techniques. It is successfully tested on a practical inverted pendulum controlled by a fault-prone DC motor. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>In this article, a simplified bidirectional associative memory network with delays involving six neurons is considered. By analyzing the distribution of roots of the characteristic equation for linearized system regarding the sum of delay as a bifurcation parameter, we obtain the condition of the occurrence for Hopf bifurcation. It reveals that Hopf bifurcation occurs when the sum of the delay passes through a critical value. The direction and the stability of the bifurcating periodic solution are determined by applying the normal form theory and center manifold theorem. Finally, a numerical example is used to illustrate the validity of theoretical results obtained. © 2015 Wiley Periodicals, Inc. Complexity 21: 9–28, 2016

]]>This article studies the problem of exponential stability for continuous-time system with multiple additive delay components. Based on the dividing of the delay and reciprocally convex combination technique, some new delay-dependent stability conditions are derived by constructing a novel Lyapunov functional. These criteria are expressed as a set of linear matrix inequalities, which can be checked using the numerically efficient Matlab LMI Control Toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 29–41, 2016

]]>Soil column depth is predicted over time scales up to a million years based on dynamics at the pore scale. The power law result integrates result for solute transport from percolation theory with typical flow velocities. Verification was based on studied soils from 14 regions worldwide over time scales from decades to a million years. The time derivative of the soil depth generates the soil production function as a function of depth. Comparison with soil production data from five locations, over similar time scales, verifies the accuracy of the predicted power to within 2%. The prediction thus unites within one framework time scales of seconds with a million years. The results allow calculation of the effects of physical soil removal on the rates of silicate weathering at the base of the column, important inputs to the global carbon cycle, neotectonics, and drainage basin evolution. © 2015 Wiley Periodicals, Inc. Complexity 21: 42–49, 2016

]]>This article is concerned with the robust stability analysis for Markovian jump systems with mode-dependent time-varying delays and randomly occurring uncertainties. Sufficient delay-dependent stability results are derived with the help of stability theory and linear matrix inequality technique using direct delay-decomposition approach. Here, the delay interval is decomposed into two subintervals using the tuning parameter η such that , and the sufficient stability conditions are derived for each subintervals. Further, the parameter uncertainties are assumed to be occurring in a random manner. Numerical examples are given to validate the derived theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 50–60, 2016

]]>We confirm that distributions of human response times have power-law tails and argue that, among closed-form distributions, the generalized inverse gamma distribution is the most plausible choice for their description. We speculate that the task difficulty tracks the half-width of the distribution and show that it is related to the exponent of the power-law tail. © 2015 Wiley Periodicals, Inc. Complexity 21: 61–69, 2016

]]>In power distribution systems, with their great vastness and various outage causes, one of the most important problems of power distribution companies is to select a suitable maintenance strategy of system elements and method of financial planning for the maintenance of system elements with the two objectives of decrease in outage costs and improvement of system reliability. In this article, a practical method is introduced for the selection of a suitable system elements maintenance strategy; moreover, to plan the preventive maintenance budget for the system elements, two methods are offered: the cost optimization method and the fuzzy Analytic Hierarchy Process (AHP) method. In the former method, a new model of system maintenance cost is offered. This model, based on system outage information, the elements maintenance costs are determined as functions of system reliability indices and preventive maintenance budget. The latter method, too, a new guideline is introduced for considering the cost and reliability criteria in the trend of preventive maintenance budget planning. In this method, the preventive maintenance budget for the elements is determined based on relative priority of elements with reliability criteria. © 2015 Wiley Periodicals, Inc. Complexity 21: 70–88, 2016

]]>We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential equations which involve parameters defined by probabilities. Society is described as an ensemble of individuals divided into income classes; the individuals exchange money through binary and ternary interactions, leaving the total wealth unchanged. The ternary interactions represent taxation and redistribution effects. Dynamics is investigated through computational simulations, the focus being on the effects that different fiscal policies and differently weighted welfare policies have on the long-run income distributions. The model provides a tool which may contribute to the identification of the most effective actions toward a reduction of economic inequality. We find for instance that, under certain hypotheses, the Gini index is more affected by a policy of reduction of the welfare and subsidies for the rich classes than by an increase of the upper tax rate. Such a policy also has the effect of slightly increasing the total tax revenue. © 2015 Wiley Periodicals, Inc. Complexity 21: 89–98, 2016

]]>Maximum Power Point Tracking (MPPT) is used in Photovoltaic (PV) systems to maximize its output power. A new MPPT system has been suggested for PV-DC motor pump system by designing two PI controllers. The first one is used to reach MPPT by monitoring the voltage and current of the PV array and adjusting the duty cycle of the DC/DC converter. The second PI controller is designed for speed control of DC series motor by setting the voltage fed to the DC series motor through another DC/DC converter. The suggested design problem of MPPT and speed controller is formulated as an optimization task which is solved by Artificial Bee Colony (ABC) to search for optimal parameters of PI controllers. Simulation results have shown the validity of the developed technique in delivering MPPT to DC series motor pump system under atmospheric conditions and tracking the reference speed of motor. Moreover, the performance of the ABC algorithm is compared with Genetic Algorithm for various disturbances to prove its robustness. © 2015 Wiley Periodicals, Inc. Complexity 21: 99–111, 2016

]]>This article addresses the distributed containment control problem in a group of agents governed by second-order dynamics with directed network topologies. Considering there are multiple leaders, we study a general second-order containment controller which can realize several different consensus modes by adjusting control gains. A necessary and sufficient condition on the control gains of the general containment controller is provided. Moreover, the delay sensitivity of the closed-loop multiagent system under the general containment controller is studied; the maximal upper bound of the constant delays is obtained. Finally, several numerical examples are used to illustrate the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 112–120, 2016

]]>The information sources using logistic maps have been studied in this article. We use a particular symmetric binary function to generate the binary sequences due to the generating partition of the logistic maps, which can reflect the dynamics of chaotic real-valued sequences. Using this binary function, we will establish a binary description of the logistic maps, and prove that this description is equivalent with the logistic maps. The probability of all the possible binary sequences generated by this symmetric binary function has been calculated according to this description. Furthermore, the cryptographic complexity of these binary sequences is evaluated theoretically and experimentally, including the correlation functions, the linear complexity, the nonlinear complexity, the Lempel–Ziv complexity and the approximate entropy. Such results show that the logistic binary sequences have good properties of cryptography. © 2015 Wiley Periodicals, Inc. Complexity 21: 121–129, 2016

]]>This article presents a novel neural network (NN) based on NCP function for solving nonconvex nonlinear optimization (NCNO) problem subject to nonlinear inequality constraints. We first apply the p-power convexification of the Lagrangian function in the NCNO problem. The proposed NN is a gradient model which is constructed by an NCP function and an unconstrained minimization problem. The main feature of this NN is that its equilibrium point coincides with the optimal solution of the original problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed NN is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, simulation results on two numerical examples and two practical examples are given to show the effectiveness and applicability of the proposed NN. © 2015 Wiley Periodicals, Inc. Complexity 21: 130–141, 2016

]]>This article investigates the delay-dependent robust dissipative sampled-data control problem for a class of uncertain nonlinear systems with both differentiable and non-differentiable time-varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed-loop system is strictly (Q, S, R)-dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_{∞} performance, passivity performance, mixed H_{∞}, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_{∞} performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_{∞} and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple-input and multiple-output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016

]]>The problem of passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time-varying delays is investigated in this article. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay-decomposing idea and using improved free-weighting matrix method, some improved delay-dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 167–179, 2016

]]>In this article, a novel four dimensional autonomous nonlinear systezm called hyperchaotic Rikitake system is proposed. Basic properties of the new system are investigated and the complex dynamical behaviors, such as time series, bifurcation diagram, and Lyapunov exponents are analyzed by dynamic analysis approaches. To control the new hyperchaotic system, the delayed feedback control is introduced. Regarding the time delay as a bifurcation parameter, stability and bifurcations with respect to time delay are investigated. Conditions assuring the existence of Hopf bifurcation and the distribution of roots to the associated characteristic equation are investigated by utilizing the polynomial theorem. Besides, the Hopf bifurcation is proved to occur when the bifurcation parameter (time delay) crosses through derived critical value. Finally, numerical simulations are provided to prove the consistence with the derived theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 180–193, 2016

]]>In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time-delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed-loop system and achieves zero-tracking error in the presence of input nonlinearity, time-delays, time-varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016

]]>Computer models can help humans gain insight into the functioning of complex systems. Used for training, they can also help gain insight into the cognitive processes humans use to understand these systems. By influencing humans understanding (and consequent actions) computer models can thus generate an impact on both these actors and the very systems they are designed to simulate. When these systems also include humans, a number of self-referential relations thus emerge which can lead to very complex dynamics. This is particularly true when we explicitly acknowledge and model the existence of multiple conflicting representations of reality among different individuals. Given the increasing availability of computational devices, the use of computer models to support individual and shared decision making could potentially have implications far wider than the ones often discussed within the Information and Communication Technologies community in terms of computational power and network communication. We discuss some theoretical implications and describe some initial numerical simulations. © 2015 Wiley Periodicals, Inc. Complexity 21: 202–213, 2016

]]>We present an individual based model of cultural evolution, where interacting agents are coded by binary strings standing for strategies for action, blueprints for products or attitudes and beliefs. The model is patterned on an established model of biological evolution, the Tangled Nature Model (TNM), where a “tangle” of interactions between agents determines their reproductive success. In addition, our agents also have the ability to copy part of each other's strategy, a feature inspired by the Axelrod model of cultural diversity. Unlike the latter, but similarly to the TNM, the model dynamics goes through a series of metastable stages of increasing length, each characterized by mutually enforcing cultural patterns. These patterns are abruptly replaced by other patterns characteristic of the next metastable period. We analyze the time dependence of the population and diversity in the system, show how different cultures are formed and merge, and how their survival probability lacks, in the model, a finite average life-time. Finally, we use historical data on the number of car manufacturers after the introduction of the automobile to the market, to argue that our model can qualitatively reproduce the flurry of cultural activity which follows a disruptive innovation. © 2015 Wiley Periodicals, Inc. Complexity 21: 214–223, 2016

]]>This article deals with the problem of control of canonical non-integer-order dynamical systems. We design a simple dynamical fractional-order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering-free fractional-order sliding mode controller. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–233, 2016

]]>This article presents a new strategy based on multistage fuzzy PID controller for damping power system stabilizer in multimachine environment using Honey Bee Mating Optimization (HBMO). The proposed technique is a new metaheuristic algorithm which is inspired by mating procedure of the honey bee. Actually, the mentioned algorithm is used recently in power systems which demonstrate the good reflex of this algorithm. Also, finding the parameters of PID controller in power system has direct effect for damping oscillation. Hence, to reduce the design effort and find a better fuzzy system control, the parameters of proposed controller is obtained by HBMO that leads to design controller with simple structure that is easy to implement. The effectiveness of the proposed technique is applied to single machine connected to infinite bus and IEEE 3–9 bus power system. The proposed technique is compared with other techniques through integral of the time multiplied absolute value of the error and figure of demerit. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–245, 2016

]]>This article is concerned with the fault-tolerant mixed /passive synchronization problem for chaotic neural networks by sampled-data control scheme. The objective is focused on the design of a reliable controller such that the mixed /passivity performance level of the resulting synchronization error system is ensured in the presence of actuator failures. A time-dependent Lyapunov functional and an improved reciprocally convex approach combined with a novel integral inequality are applied to optimize the availability of the information on the actual sampling pattern. Then, some sufficient conditions of mixed /passivity performance analysis for the synchronization error systems are derived. A desired reliable sampled-data controller is designed by solving the optimization problems. Finally, to demonstrate the effectiveness of the proposed method, a practical chaotic neural networks is provided. © 2015 Wiley Periodicals, Inc. Complexity 21: 246–259, 2016

]]>In recent years, control of nonlinear complex predator–prey systems has attracted the attention of many researchers. The previous works have some weaknesses such as neglecting the consideration of the effects of both model uncertainties and unknown parameters and having an infinite time of convergence. To overcome the mentioned shortages, this article solves the problem of robust control of nonlinear complex Holling type II predator–prey system in a given finite time. It is assumed that the parameters of the system are fully unknown in advance and some uncertainties perturb the system's dynamics. To tackle the system unknown parameters, some adaptation laws are introduced. Thereafter, a robust switching controller is proposed to finite-timely stabilize the predator–prey system. An illustrative example demonstrates the efficiency and usefulness of the proposed control strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 260–266, 2016

]]>Cellular automata (CA) are discrete dynamical systems that, out of the fully local action of its state transition rule, are capable of generating a multitude of global patterns, from the trivial to the arbitrarily complex ones. The set of global configurations that can be obtained by iterating a one-dimensional cellular automaton for a finite number of times can always be described by a regular language. The size of the minimum finite automaton corresponding to such a language at a given time step provides a complexity measure of the underlying rule. Here, we study the time evolution of elementary CA, in terms of such a regular language complexity. We review and expand the original results on the topic, describe an alternative method for generating the subsequent finite automata in time, and provide a method to analyze and detect patterns in the complexity growth of the rules. © 2015 Wiley Periodicals, Inc. Complexity 21: 267–279, 2016

]]>Describing the dynamics of a city is a crucial step to both understanding the human activity in urban environments and to planning and designing cities accordingly. Here, we describe the collective dynamics of New York City (NYC) and surrounding areas as seen through the lens of Twitter usage. In particular, we observe and quantify the patterns that emerge naturally from the hourly activities in different areas of NYC, and discuss how they can be used to understand the urban areas. Using a dataset that includes more than 6 million geolocated Twitter messages we construct a movie of the geographic density of tweets. We observe the diurnal “heartbeat” of the NYC area. The largest scale dynamics are the waking and sleeping cycle and commuting from residential communities to office areas in Manhattan. Hourly dynamics reflect the interplay of commuting, work and leisure, including whether people are preoccupied with other activities or actively using Twitter. Differences between weekday and weekend dynamics point to changes in when people wake and sleep, and engage in social activities. We show that by measuring the average distances to a central location one can quantify the weekly differences and the shift in behavior during weekends. We also identify locations and times of high Twitter activity that occur because of specific activities. These include early morning high levels of traffic as people arrive and wait at air transportation hubs, and on Sunday at the Meadowlands Sports Complex and Statue of Liberty. We analyze the role of particular individuals where they have large impacts on overall Twitter activity. Our analysis points to the opportunity to develop insight into both geographic social dynamics and attention through social media analysis. © 2015 Wiley Periodicals, Inc. Complexity 21: 280–287, 2016

]]>This article proposed a new control strategy based on Takagi–Sugeno fuzzy model for deceasing the power system oscillation. This controller is based on the parallel distributed compensation structure, the stability of the whole closed-loop model is provided using a general Lyapunov-Krasovski functional. Also, in this article, a new objective function has been considered to test the proposed Fuzzy Power System Stabilizer in different load conditions which increase the system damping after the system undergoes a disturbance. So, for testing the effectiveness of the proposed controller, the damping factor, damping ratio, and a combination of the damping factor and damping ratio were analyzed and compared with the proposed objective function. The effectiveness of the proposed strategy has been used over 16 machine 68 bus power system. The eigenvalue analysis and nonlinear time domain simulation results proof the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 288–298, 2016

]]>This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3-machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve-point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016

]]>This study proposes a new set of measures for longitudinal social networks (LSNs). A LSN evolves over time through the creation and/or deletion of links among a set of actors (e.g., individuals or organizations). The current literature does feature some methods, such as multiagent simulation models, for studying the dynamics of LSNs. These methods have mainly been utilized to explore evolutionary changes in LSNs from one state to another and to explain the underlying mechanisms for these changes. However, they cannot quantify different aspects of a LSN. For example, these methods are unable to quantify the level of dynamicity shown by an actor in a LSN and its contribution to the overall dynamicity shown by that LSN. This article develops a set of measures for LSNs to overcome this limitation. We illustrate the benefits of these measures by applying them to an exploration of the Enron crisis. These measures successfully identify a significant but previously unobserved change in network structures (both at individual and group levels) during Enron's crisis period. © 2015 Wiley Periodicals, Inc. Complexity 21: 309–320, 2016

]]>Membrane fission is a process by which a biological membrane is split into two new ones in the manner that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication rules of length at most two, and we prove the computational efficiency of this kind of models when using communication rules of length at most three. Hence, a sharp borderline between tractability and **NP**–hardness is provided in terms of the length of communication rules. © 2015 Wiley Periodicals, Inc. Complexity 21: 321–334, 2016

Several important properties of chaos synchronization of bidirectional coupled systems remain still unexplored. This article investigates synchronization behavior for chaotic systems subject to states quantization. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed to strictly synchronize chaotic systems via limited capacity communication channels. Furthermore, it is important to point out that the mutual synchronization behavior for bidirectional coupled systems is determined by the amount of transmitting information and the initial states of coupled systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 335–342, 2016

]]>This article is concerned with the problem of synchronization between two uncertain complex-variable chaotic systems with parameters perturbation and discontinuous unidirectional coupling. Based on the stability theory and comparison theorem of differential equations, some sufficient conditions for the complete synchronization and generalized synchronization are obtained. The theoretical results show that the two uncertain complex-variable chaotic systems with discontinuous unidirectional coupling can achieve synchronization if the time-average coupling strength is large enough. Finally, numerical examples are examined to illustrate the feasibility and effectiveness of the analytical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 343–355, 2016

]]>This article presents a nonlinear state feedback stabilizer using linear matrix inequalities for a class of uncertain nonlinear systems with Lipschitz nonlinearities. The proposed controller improves the transient performance and steady state accuracy simultaneously. To improve the stabilization performance, a nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. Simulation results are presented to show the effectiveness of the offered method. © 2015 Wiley Periodicals, Inc. Complexity 21: 356–362, 2016

]]>In this article, an adaptive sliding mode technique based on a fractional-order (FO) switching type control law is designed to guarantee robust stability for a class of uncertain three-dimensional FO nonlinear systems with external disturbance. A novel FO switching type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criteria of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. Effectiveness of the proposed control scheme is illustrated through numerical simulations. © 2015 Wiley Periodicals, Inc. Complexity 21: 363–373, 2016

]]>Murphy's Law is not a law in the formal sense yet popular science often compares it with the Second Law of Thermodynamics as both the statements point toward a more disorganized state with time. In this article, we first construct a mathematically equivalent statement for Murphy's Law and then disprove it using the intuitive idea that energy differences will level off along the paths of steepest descent, or along trajectories of least action. © 2015 Wiley Periodicals, Inc. Complexity 21: 374–380, 2016

]]>This article focuses on the problem of Guaranteed cost synchronization of complex networks with uncertainties and time-Varying delays. Sufficient conditions for the existence of the optimal guaranteed cost control laws are introduced in the light of linear matrix inequalities via the Lyapunov–Krasovskii stability theory. The time-varying node delays and time-varying coupling delays are simultaneously regarded in the complex network. The node uncertainties and coupling uncertainties are simultaneously considered as well. Numerical simulations are provided to account for the effectiveness and robustness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works. © 2015 Wiley Periodicals, Inc. Complexity 21: 381–395, 2016

]]>This article deals with the problem of nonfragile *H*_{∞} output tracking control for a kind of singular Markovian jump systems with time-varying delays, parameter uncertainties, network-induced signal transmission delays, and data packet dropouts. The main objective is to design mode-dependent state-feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed-loop networked control system tracks the output of a given reference system with the required *H*_{∞} output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode-dependent and delay-dependent conditions are obtained to guarantee the augmented output tracking closed-loop system is not only stochastically admissible but also satisfies a prescribed *H*_{∞}-norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state-feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016

Attention deficit hyperactivity disorder (ADHD) is characterized by decreased attention span, impulsiveness, and hyperactivity. Autonomic nervous system imbalance was previously described in this population. We aim to compare the autonomic function of children with ADHD and controls by analyzing heart rate variability (HRV). Children with ADHD (22 boys, mean age 9.964 years) and 28 controls (15 boys, mean age 9.857 years) rested in supine position with spontaneous breathing for 20 min. Heart rate was recorded beat by beat. HRV analysis was performed by use of chaotic global techniques. ADHD promoted an increase in the chaotic forward parameter. The algorithm which applied all three chaotic global parameters was only the second optimum statistically measured by Kruskal–Wallis (P < 0.0001) and low standard deviations. It was also highly influential by principal component analysis with almost all variation covered by the first two components. The third algorithm which lacked the (high spectral Detrended Fluctuation Analysis) parameter performed best statistically. However, we chose the algorithm which applied all three chaotic globals due to previous studies mentioned in the text—forward and inverse problems. Comparison of the autonomic function by analyzing HRV with chaotic global techniques suggests an increase in chaotic activity in children with ADHD in relation to the control group. © 2015 Wiley Periodicals, Inc. Complexity 21: 412–419, 2016

]]>This article addresses the problem of fault-tolerant sampled-data mixed and passivity control for a class of stochastic system with actuator failures, where the plant is modeled as a continuous-time one and the control inputs are implemented as discrete-time signals. Sufficient conditions for the reliable sampled-data mixed and passivity performance control law is established for the considered systems by constructing an appropriate Lyapunov–Krasovskii functional together with the Newton–Leibniz formula and free-weighting matrix technique. More precisely, linear matrix inequality based sampled-data methodology is employed to design the mixed and passivity formation controller to reject the impact of the formation changes being treated as disturbances. Simulation studies are performed based on the flight control model to verify the stability, performance, and effectiveness of the proposed design strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 420–429, 2016

]]>In this article, synchronization problem of master–slave system with phase-type semi-Markovian switching is investigated via sliding mode control scheme. By utilizing a supplementary variable technique and a plant transformation, the master–slave semi-Markovian switching system can be equivalently expressed as its associated Markovian switching system. Then an integral sliding surface is constructed to guarantee stochastic synchronization of master–slave semi-Markovian switching system, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. Finally, numerical simulations are presented to show the effectiveness of the proposed sliding-mode design scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 430–441, 2016

]]>Our aim in this work was to examine the model underpinning the spread of the Rubella virus using the novel derivative called beta-derivative. The study of the equilibrium points together with the analysis of the disease free equilibrium points was presented. Due to the complexity of the modified equation, we introduced a new operator based on the Sumudu transform. The properties of this operator were proposed and proved in detail. We made used of this operator together with the idea of perturbation method to derive a special solution of the extended model. The stability of the method for solving this model was presented. The uniqueness of the special solution was presented, and numerical simulations were done. The graphical representations show that the model depends on both parameters and the fractional order. © 2015 Wiley Periodicals, Inc. Complexity 21: 442–451, 2016

]]>Locating an unknown object position in a map by information stored in the unconscious mind is important from practical point of view. Locating captives, bomb, or terrorist secret bases by interrogation is problem that the intelligent agencies face daily. The person interrogated may have the desired information stored in unconscious or may not know it at all. In this article, we will present a novel way of retrieving the object location based on eye movement. The technique is based on a Bayesian mathematical approach to localization, in which measured count rates of eye fixation and duration, the probability of the location of the target is correlated with the count rate and drops as the distance increases from the fixation location. We focused on the discrete model and then generalized it to continuous model. © 2015 Wiley Periodicals, Inc. Complexity 21: 452–459, 2016

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