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 21: 13–23, 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 21: 24–32, 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 21: 33–41, 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 21: 42–53, 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 21: 54–66, 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 21: 67–72, 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 21: 73–98, 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 21: 99–112, 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 21: 113–122, 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 21: 123–137, 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 21: 138–150, 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 21: 151–155, 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 21: 156–164, 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 21: 165–177, 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 21: 178–190, 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 21: 191–200, 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 21: 201–206, 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 21: 207–234, 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 21: 235–242, 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 21: 243–248, 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 21: 249–258, 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 21: 259–267, 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 21: 268–288, 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 21: 289–295, 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 21: 296–308, 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 21: 309–319, 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 21: 320–328, 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 21: 329–341, 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 21: 342–354, 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 21: 355–369, 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 21: 370–379, 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 21: 380–387, 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 21: 388–396, 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 21: 397–408, 2016

]]>Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts from realistic cognitive pressures, (2) it does not require fine tuning of parameters, and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws. Our findings suggest that the recurrence of Zipf's law in human languages could originate from pressure for easy and fast communication. © 2016 Wiley Periodicals, Inc. Complexity 21: 409–411, 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 21: 412–426, 2016

*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 21: 427–437, 2016

In this article, the problem of global exponential stability in Lagrange sense of neutral type complex-valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay-dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016

]]>Bus transportation is the most convenient and cheapest way of public transportation in Indian cities. Due to cost-effectiveness and wide reachability, buses bring people to their destinations every day. Although the bus transportation has numerous advantages over other ways of public transportation, this mode of transportation also poses a serious threat of spreading contagious diseases throughout the city. It is extremely difficult to predict the extent and spread of such an epidemic. Earlier studies have focused on the contagion processes on scale-free network topologies; whereas, real-world networks such as bus networks exhibit a wide-spectrum of network topology. Therefore, we aim in this study to understand this complex dynamical process of epidemic outbreak and information diffusion on the bus networks for six different Indian cities using SI and SIR models. We identify epidemic thresholds for these networks which help us in controlling outbreaks by developing node-based immunization techniques. © 2016 Wiley Periodicals, Inc. Complexity 21: 451–458, 2016

]]>This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016

]]>In this article, we study a new hybrid synchronization scheme for two different delayed dynamical networks with nonidentical topologies and mixed coupling. Based on Barbalat lemma and Schur complement lemma, some hybrid synchronization criteria are achieved via the open-loop-plus-pinning adaptive control strategy. Two numerical examples with two types of node dynamics illustrate the effectiveness of the proposed synchronous criteria. © 2016 Wiley Periodicals, Inc. Complexity 21: 470–482, 2016

]]>Most loads in the power distribution system of Tehran Metro (Subway) are inductive and lead to poor power factor (PF) especially in Lighting and Power Substation. One of the methods of PF correction is adding or producing the capacitive components within the circuit to eliminate the effect of inductive loads. Optimal capacitor placement (OCP), with the objects of power system voltage profile improvement, PF correction, loss reduction, and line reactive power decrease are of particular importance in power system control and planning. These objects depend on how the capacitive components are installation and to achieve them, since the capacitor placement is nonlinear problem and has some equally and inequality constraint. This article investigates OCP in the actual power distribution grid of Tehran Metro (Line 2) in the presence of nonlinear loads. The placement problem is solved using Genetic Algorithms as implemented in the Electrical Transient Analyser Program software. Results (capacity release, total generation, loading, demand, power losses and number of capacitor banks, costs and annual benefits) are obtained and analysed. This study and simulation shows that by OCP can calculate reduce annual losses and release capacity of equipment in power distribution grid of Tehran Metro such as cables and transformers from reactive power and that will maximize profits. © 2016 Wiley Periodicals, Inc. Complexity 21: 483–493, 2016

]]>This article focus on optimal economic load dispatch based on an intelligent method of shark smell optimization (SSO). In this problem, the risk constrains has been considered which has root in uncertainity and unpredictable behavior of wind power. Regarding to increasing of this clean energy in power systems and un-dispatchable behavior of wind power, its conditional value at risk index considered in this article which consists of loss from load and "spilling" wind energy connected with unpredictable imbalances among generation and load. This problem has been considered as an optimization problem based on SSO that evaluate the balance between cost and risk. This algorithm is based on distinct shark smell abilities for localizing the prey. In sharks' movement, the concentration of the odor is an important factor to guide the shark to the prey. In other words, the shark moves in the way with higher odor concentration. This characteristic is used in the proposed SSO algorithm to find the solution of an optimization problem. Effectiveness of the proposed method has been applied over 30-bus power system in comparison with other techniques. © 2016 Wiley Periodicals, Inc. Complexity 21: 494–506, 2016

]]>The current study is focused on the state estimator design for the discrete-time complex networks with sensor failures and randomly varying nonlinearities. Bernoulli process is adopted to describe the randomly varying nonlinearities, and the norm-bounded uncertain model is used to deal with the sensor failures. Then, a set of sufficient conditions are provided to guarantee that the estimation error system is stochastically stable with the prescribed property. Then, using the linear matrix inequality method, the estimator gains are obtained. Finally, the effectiveness of the proposed new design method is illustrated through a numerical example. © 2016 Wiley Periodicals, Inc. Complexity 21: 507–517, 2016

]]>In this article, based on sampled-data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input-delay approach, the sampled-data system is equivalently transformed into a continuous-time system with a variable time delay. The main objective is to design a suitable reliable sampled-data state feedback controller guaranteeing the asymptotic stability of the resulting closed-loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger-based double integral inequality, some new delay-dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016

]]>This article addresses the stock market as a complex system. The complexity of the stock market arises from the structure of the environment, agent heterogeneity, interactions among agents, and interactions with market regulators. We develop the idea of a meta-model, which is a model of models represented in an agent-based model that allows us to investigate this type of market complexity. The novelty of this article is the incorporation of various complexities captured by network theoretical models or induced by investment behavior. The model considers agents heterogeneous in terms of their strategies and investment behavior. Four investment strategies are included in the model: zero-intelligence, fundamental strategy, momentum (trend followers), and adaptive trading strategy using the artificial neural network algorithm. In terms of behavior, the agents can be risk averse or loss occupied with overconfidence or conservative biases. The agents may interact with each other by sharing market sentiments through a structured scale-free network. The market regulator controls the market through various control tools such as the risk-free rate and taxation. Parameters are calibrated to the S&P500. The calibration is implemented using a scatter search heuristic approach. The model is validated using various stylized facts of stock return patterns such as excess kurtosis, auto-correlation, and ARCH effect phenomena. Analysis at the macro and micro level of the market was performed by measuring the sensitivity of volatility and market capital and investigating the wealth distributions of the agents. We found that volatility is more sensitive to the model parameters than to market capital, and thus, the level of volatility does not affect market capital. In addition, the findings suggest that the efficient market hypothesis holds at the macro level but not at the micro level. © 2016 Wiley Periodicals, Inc. Complexity 21: 530–554, 2016

]]>This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time-varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay-dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water-quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016

]]>This article investigates the problem of robust dissipative fault-tolerant control for discrete-time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay-dependent sufficient conditions is developed for achieving the required result. A design scheme for the state-feedback reliable dissipative
controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed-loop system with actuator failures. In addition, the proposed controller not only stabilize the fault-free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_{∞} control, passivity control, and mixed H_{∞} and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault-tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid-coupled dynamical network with time-varying internal delay and time-varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning-control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer-synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned-node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non-fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016

]]>This paper proposes a novel T-S fuzzy control method instead of the traditional linear system control method to improve the TCP network performance. Thus a TCP network can be modeled as a T-S fuzzy system, and by use of linear matrix inequality method and cone complementarity linearization algorithm, a fuzzy state feedback controller is provided while considering the problem of the asynchronous membership grades between the controller and the plant. Simulation results are presented to show that the proposed control approach can guarantee the asymptotical stability of the studied system and the desired queue size. © 2016 Wiley Periodicals, Inc. Complexity 21: 606–612, 2016

]]>Imperial Rome with its >50% assassination rate of emperors, many of whom are depicted in history as ‘deranged’, initially appears a chaotic period of history beyond the purview of science. But time series analysis indicates this violence occurred non-randomly: reign length was autocorrelated and demonstrated ‘memory persistence,’ and short reigns occurred in clusters. Additionally, deviations from average reign-length occurred in patterns matching the Empire's rise and decline. A model is proposed for how army-backed usurpation and post-coup instability likely generated the observed cycles. The five-century span of Imperial Rome likely makes it the longest-lived regime with fair documentation, and potentially provides a ‘laboratory’ with ongoing relevance for studying transmission of violence and instability. © 2016 Wiley Periodicals, Inc. Complexity 21: 613–622, 2016

]]>This article is concerned with observer and controller design for networked control systems, where the considered plant refers to a class of discrete-time communication delay Markovian jump systems. In the study, random packet losses and output quantization are considered simultaneously. The packet losses considered here includes sensor to controller and controller to actuator sides, which are modeled as two Bernoulli distributed white sequences, respectively. An observer-based control scheme is developed to stabilize the closed-loop systems. Finally, an illustrative example is provided to show the applicability of the proposed control method. © 2016 Wiley Periodicals, Inc. Complexity 21: 623–634, 2016

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