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

]]>This article designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern classification. To design the classifier, (1) we first identify a set of ACAs that always converge to fixed points from any seeds, (2) each ACA should have at least two but not huge number of fixed point attractors, and (3) the convergence time of these ACAs are not to be exponential. To address the second issue, we propose a graph, coined as fixed point graph of an ACA that facilitates in counting the fixed points. We further perform an experimental study to estimate the convergence time of ACAs, and find there are some convergent ACAs which demand exponential convergence time. Finally, we identify there are 73 (out of 256) ACAs which can be effective candidates as pattern classifier. We use each of the candidate ACAs on some standard datasets, and observe the effectiveness of each ACAs as pattern classifier. It is observed that the proposed classifier is very competitive and performs reliably better than many standard existing classifier algorithms. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s-impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity, 2016

]]>Goods, styles, ideologies are adopted by society through various mechanisms. In particular, adoption driven by innovation is extensively studied by marketing economics. Mathematical models are currently used to forecast sales of innovative goods. Inspired by the theory of diffusion processes developed for marketing economics, we propose a modelling framework for the mechanism of fashion, which we apply to first names. Analyses of French, Dutch, and US national databases validate our modelling approach for thousands of first names, covering, on average, more than 50% of the yearly incidence in each database. In these cases, it is thus possible to study how first names become popular and when they run out of fashion. Furthermore, we uncover a clear distinction between popularity and fashion: less popular names, typically not included in studies of fashion, may be driven by fashion, as well. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code, and two human natural languages were studied at the scale of characters, words, and at the Fundamental Scale resulting from adjusting the symbols length used to interpret each text-description until it produced minimum entropy. The results show that the Fundamental Scale method is comparable to using words when measuring entropy levels in written texts. However, the Fundamental Scale can also be used to analyze communication systems lacking conventional words, such as music. Measuring symbolic entropy at the fundamental scale allows to calculate quantitatively, relative levels of complexity for different communication systems. Here, we showed that music and written language share some characteristics as communication systems but differ in others. The results open novel vistas on the similarities and differences among the structure of the various communication systems that are used by humans and by nature in general. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>Complexity in nature is astounding yet the explanation lies in the fundamental laws of physics. The Second Law of Thermodynamics and the Principle of Least Action are the two theories of science that have always stood the test of time. In this article, we use these fundamental principles as tools to understand how and why things happen. In order to achieve that, it is of absolute necessity to define things precisely yet preserving their applicability in a broader sense. We try to develop precise, mathematically rigorous definitions of the commonly used terms in this context, such as action, organization, system, process, etc., and in parallel argue the behavior of the system from the first principles. This article, thus, acts as a mathematical framework for more discipline-specific theories. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, we propose a Cucker–Smale-type self-propelled particle model with continuous non-Lipschitz protocol. We show that the flocking can occur in finite time if the communication rate function satisfies a lower bound condition. Both our theoretical and numerical results uncover a power-law relationship between the convergence time and the number of individuals. Our result implies that the individuals in groups with high density can transit rapidly to ordered collective motion. We also investigate the influence of control parameter on the convergence speed. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>Allostatic load (AL) is a complex clinical construct, providing a unique window into the cumulative impact of stress. However, due to its inherent complexity, AL presents two major measurement challenges to conventional statistical modeling (the field's dominant methodology): it is comprised of a complex causal network of bioallostatic systems, represented by an even larger set of dynamic biomarkers; and, it is situated within a web of antecedent socioecological systems, linking AL to differences in health outcomes and disparities. To address these challenges, we employed case-based computational modeling (CBM), which allowed us to make four advances: (1) we developed a multisystem, 7-factor (20 biomarker) model of AL's network of allostatic systems; (2) used it to create a catalog of nine different clinical AL profiles (causal pathways); (3) linked each clinical profile to a typology of 23 health outcomes; and (4) explored our results (post hoc) as a function of gender, a key socioecological factor. In terms of highlights, (a) the Healthy clinical profile had few health risks; (b) the pro-inflammatory profile linked to high blood pressure and diabetes; (c) Low Stress Hormones linked to heart disease, TIA/Stroke, diabetes, and circulation problems; and (d) high stress hormones linked to heart disease and high blood pressure. Post hoc analyses also found that males were overrepresented on the High Blood Pressure (61.2%), Metabolic Syndrome (63.2%), High Stress Hormones (66.4%), and High Blood Sugar (57.1%); while females were overrepresented on the Healthy (81.9%), Low Stress Hormones (66.3%), and Low Stress Antagonists (stress buffers) (95.4%) profiles. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>There are occasions when people want to optimize the initial setting of a CAS (complex adaptive system) so that it evolves in a desired direction. A CAS evolves by heterogeneous actors interacting with each other. It is difficult to describe the evolution process with an objective function. Researchers usually attempt to optimize an intervening objective function, which is supposed to help a CAS evolve in a desired direction. This article puts forward an approach to optimize the initial setting of a CAS directly (instead of through an intervening objective function) by nesting agent-based simulations in a genetic algorithm. In the approach, an initial setting of a CAS is treated as a genome, and its fitness is defined by the closeness between the simulation result and the desired evolution. We test the applicability of the proposed approach on the problem of optimizing the layout of initial AFV (alternative fuel vehicle) refueling stations to maximize the diffusion of AFVs. Computation experiments show that the initial setting generated with the approach could better induce the desired evolving result than optimizing an intervening objective function. The idea of the approach can also be applied to other decision making associated with a complex adaptive process. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In the context of cognition, categorization is the process through which several elements (i.e., words) are grouped into a single set which by naming becomes an abstraction of its elements. For example, tiger, kitty, and max can be categorized as Cats. In this article, we aim to show how the physical, biological and cognitive dimensions are related in the process of categorization or abstraction through the physics of computation. Drawing on Landauer's principle, we show that the price paid in terms of entropy is higher when grouping elements of low ranking (high probability) than when grouping elements of high ranking (low probability). Therefore, the logic of the cognitive process of abstraction is explained through constraints imposed by memory on the computation of categories. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable-structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>The problem of finite-time lag synchronization of delayed neural networks via periodically intermittent control is studied. In two sections, based on the same finite-time stability theory and using the same sliding mode control, by designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws, we achieve the finite-time lag synchronization between two time delayed networks. In addition, we ensure that the trajectory of the error system converges to a chosen sliding surface within finite time and keeps it on forever. Finally, two examples are presented to verify the effectiveness of the analytical results obtained here. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This work shows how to measure composer style's comprehensiveness by performing measurements on Barlow and Morgenstern dictionary of 10, 000 classical themes. This measure can partially reveal the degree of complexity of works by Mozart as well as many greater composers. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This paper deals with how to determine which features should be included in the software to be developed. Metaheuristic techniques have been applied to this problem and can help software developers when they face contradictory goals. We show how the knowledge and experience of human experts can be enriched by these techniques, with the idea of obtaining a better requirements selection than that produced by expert judgment alone. This objective is achieved by embedding metaheuristics techniques into a requirements management tool that takes advantage of them during the execution of the development stages of any software development project. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>Conscious experience is awash with underlying relationships. Moreover, for various brain regions such as the visual cortex, the system is biased toward some states. Representing this bias using a probability distribution shows that the system can define expected quantities. The mathematical theory in this article links these facts using expected float entropy (efe), which is a measure of the expected amount of information needed, to specify the state of the system, beyond what is already known about the system from relationships that appear as parameters. Under the requirement that the relationship parameters minimize efe, the brain defines relationships. It is proposed that when a brain state is interpreted in the context of these relationships the brain state acquires meaning in the form of the relational content of the associated experience. For a given set, the theory represents relationships using weighted relations which assign continuous weights, from 0 to 1, to the elements of the Cartesian product of that set. The relationship parameters include weighted relations on the nodes of the system and on their set of states. Examples obtained using Monte-Carlo methods (where relationship parameters are chosen uniformly at random) suggest that efe distributions with long left tails are most important. © 2015 The Authors. Complexity Published by Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, the nonfragile passivity and passification problems are investigated for a class of nonlinear singular networked control systems (NCSs) with network-induced time-varying delay. In particular, the randomly occurring controller gain fluctuation is taken into consideration by introducing the stochastic variable satisfying the Bernoulli random distribution. By constructing proper Lyapunov–Krasovskii function, delay-dependent sufficient conditions are established to guarantee the passivity of the singular NCSs. Based on the derived results, the nonfragile passification controller is further designed in terms of linear matrix inequalities. Finally, a numerical example is provided to illustrate the applicability and effectiveness of our theoretical results. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This article addresses the synchronization of nonlinear master–slave systems under input time-delay and slope-restricted input nonlinearity. The input nonlinearity is transformed into linear time-varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple-integral-based Lyapunov–Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay-range-dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope-restricted nonlinearity. Further, time-delays are treated using an advanced delay-range-dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In many control engineering applications, it is impossible or expensive to measure all the states of the dynamical system and only the system output is available for controller design. In this study, a new dynamic output feedback control algorithm is proposed to stabilize the unstable periodic orbit of chaotic spinning disks with incomplete state information. The proposed control structure is based on the T-S fuzzy systems. This investigation also introduces a new design procedure to satisfy a constraint on the T-S fuzzy dynamic output feedback control signal. This procedure is independent of the exact value of initial states. Finally, computer simulations are accomplished to illustrate the performance of the proposed control algorithm. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here, we prove based on an analysis of the information that can be obtained from experimental observations that theory is even more essential in the understanding of complex systems. Implications of this proof revise the general understanding of how we can understand complex systems including the behaviorist approach to human behavior, problems with testing engineered systems, and medical experimentation for evaluating treatments and the Food and Drug Administration approval of medications. Each of these approaches are inherently limited in their ability to characterize real world systems due to the large number of conditions that can affect their behavior. Models are necessary as they can help to characterize behavior without requiring observations for all possible conditions. The testing of models by empirical observations enhances the utility of those observations. For systems for which adequate models have not been developed, or are not practical, the limitations of empirical testing lead to uncertainty in our knowledge and risks in individual, organizational, and social policy decisions. These risks should be recognized and inform our decisions. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>We investigate the effect of the literature suggested optimal values of the parameters of a dynamic decision-making heuristic in the presence of semirationally managed supply chain echelons using a soft coded one-to-one version of The Beer Game as an experimental platform. According to the counterintuitive results obtained in this study, it is possible for a “rational manager” to obtain higher costs than the costs generated by a “semirational manager.” Thus, the results do not support the use of the well-established decision parameter values for the echelon of concern if the other echelons' inventories are managed suboptimally. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In the health informatics era, modeling longitudinal data remains problematic. The issue is method: health data are highly nonlinear and dynamic, multilevel and multidimensional, comprised of multiple major/minor trends, and causally complex—making curve fitting, modeling, and prediction difficult. The current study is fourth in a series exploring a case-based density (CBD) approach for modeling complex trajectories, which has the following advantages: it can (1) convert databases into sets of cases (k dimensional row vectors; i.e., rows containing k elements); (2) compute the trajectory (velocity vector) for each case based on (3) a set of bio-social variables called traces; (4) construct a theoretical map to explain these traces; (5) use vector quantization (i.e., k-means, topographical neural nets) to longitudinally cluster case trajectories into major/minor trends; (6) employ genetic algorithms and ordinary differential equations to create a microscopic (vector field) model (the inverse problem) of these trajectories; (7) look for complex steady-state behaviors (e.g., spiraling sources, etc) in the microscopic model; (8) draw from thermodynamics, synergetics and transport theory to translate the vector field (microscopic model) into the linear movement of macroscopic densities; (9) use the macroscopic model to simulate known and novel case-based scenarios (the forward problem); and (10) construct multiple accounts of the data by linking the theoretical map and k dimensional profile with the macroscopic, microscopic and cluster models. Given the utility of this approach, our purpose here is to organize our method (as applied to recent research) so it can be employed by others. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, based on the stability theory of fractional-order systems, chaos synchronization is achieved in the fractional-order modified Van der Pol–Duffing system via a new linear control approach. A fractional backstepping controller is also designed to achieve chaos synchronization in the proposed system. Takagi-Sugeno fuzzy models-based are also presented to achieve chaos synchronization in the fractional-order modified Van der Pol–Duffing system via linear control technique. Numerical simulations are used to verify the effectiveness of the synchronization schemes. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, we infer inequalities representing (upper) bounds for real quantities. The obtained bound is parametric and, hence, it might be applicable to special problems. Here, we apply it to probabilities assigned to complex networks. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite-time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well-known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–19, 2016

]]>The significant characteristic of the TODIM (an acronym in Portuguese of Interactive and Multiple Attribute Decision Making) method is that it can consider the bounded rationality of the decision makers. However, in the classical TODIM method, the rating of the attributes only can be used in the form of crisp numbers. Because 2-dimension uncertain linguistic variables can easily express the fuzzy information, in this article, we extend the TODIM method to 2-dimension uncertain linguistic information. First of all, the definition, characteristics, expectation, comparative method and distance of 2-dimension uncertain linguistic information are introduced, and the steps of the classical TODIM method for Multiple attribute decision making (MADM) problems are presented. Second, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the form of 2-dimension uncertain linguistic variables, and detailed decision steps are given. Its significant characteristic is that it can fully consider the bounded rationality of the decision makers, which is a real action in real decision making. Finally, a numerical example is provided to verify the developed approach and its practicality and effectiveness. © 2014 Wiley Periodicals, Inc. Complexity 21: 20–30, 2016

]]>Filtration combustion (FC) is described by Laplacian growth without surface tension. These equations have elegant analytical solutions that replace the complex integro-differential motion equations by simple differential equations of pole motion in a complex plane. The main problem with such a solution is the existence of finite time singularities. To prevent such singularities, nonzero surface tension is usually used. However, nonzero surface tension does not exist in FC, and this destroys the analytical solutions. However, a more elegant approach exists for solving the problem. First, we can introduce a small amount of pole noise to the system. Second, for regularization of the problem, we throw out all new poles that can produce a finite time singularity. It can be strictly proved that the asymptotic solution for such a system is a single finger. Moreover, the qualitative consideration demonstrates that a finger with of the channel width is statistically stable. Therefore, all properties of such a solution are exactly the same as those of the solution with nonzero surface tension under numerical noise. The solution of the Saffman–Taylor problem without surface tension is similar to the solution for the equation of cellular flames in the case of the combustion of gas mixtures. © 2014 Wiley Periodicals, Inc. Complexity 21: 31–42, 2016

]]>This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive–impulsive controller and the parameters adaptive laws are designed via the discrete-time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the well-known delayed Lü chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. © 2014 Wiley Periodicals, Inc. Complexity 21: 43–51, 2016

]]>To analyze the complexity of continuous chaotic systems better, the modified multiscale permutation entropy (MMPE) algorithm is proposed. Characteristics and parameter choices of the MMPE algorithm are investigated. The comparative study between MPE and MMPE shows that MMPE has better robustness for identifying different chaotic systems when the scale factor τ takes large values. Compared with MPE, MMPE algorithm is more suitable for analyzing the complexity of time series as it has τ time series. For its application, MMPE algorithm is used to calculate the complexity of multiscroll chaotic systems. Results show that complexity of multiscroll chaotic systems does not increase as scroll number increases. Discussions based on first-order difference operation present a reasonable explanation on why the complexity does not increase. This complexity analysis method lays a theoretical as well as experimental basis for the applications of multiscroll chaotic systems. © 2014 Wiley Periodicals, Inc. Complexity 21: 52–58, 2016

]]>This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time-varying delays. The jumping parameters are represented as a continuous-time discrete-state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time-varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay-dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016

]]>This study estimates the parameters of a power law fit of the distribution of log returns of exchange traded funds (ETFs) before, during, and after the recent financial crisis. It is found, that there is considerable variation both between ETFs and between calm and turbulent phases. Exponents of the daily log return distribution are estimated to lie mostly between 3.0 and 5.0 depending on the ETF. In minute-by-minute, trading data much lower power law exponents have been found concentrating between 3.0 and 4.0 and sometimes dropping to values close to or below 3.0. Further, there is evidence for changes in the distribution during times of turbulence (value of the exponent, improvement in the goodness of fit measures of the distribution). It can be hypothesized that effects such as, infinite variance (for α < 3) or changes in the form of the distribution can occur, in turn affecting the predictability of the system which has implications for the possibility to control or regulate financial markets under such conditions. © 2014 Wiley Periodicals, Inc. Complexity 21: 73–83, 2016

]]>An exploratory study is made on the dynamics of the map defining the Mandelbrot set endowed with memory (m) of past iterations, that is, , . © 2014 Wiley Periodicals, Inc. Complexity 21: 84–96, 2016

]]>In this article, a new metaheuristic optimization algorithm is introduced. This algorithm is based on the ability of shark, as a superior hunter in the nature, for finding prey, which is taken from the smell sense of shark and its movement to the odor source. Various behaviors of shark within the search environment, that is, sea water, are mathematically modeled within the proposed optimization approach. The effectiveness of the suggested approach is compared with many other heuristic optimization methods based on standard benchmark functions. Also, to illustrate the efficiency of the proposed optimization method for solving real-world engineering problems, it is applied for the solution of load frequency control problem in electrical power systems. The obtained results confirm the validity of the proposed metaheuristic optimization algorithm. © 2014 Wiley Periodicals, Inc. Complexity 21: 97–116, 2016

]]>In this article, a novel sliding mode control (SMC) approach is proposed for the control of a class of underactuated systems which are featured as in cascaded form with external disturbances. The asymptotic stability conditions on the error dynamical system are expressed in the form of linear matrix inequalities. The control objective is to construct a controller such that would force the state trajectories to approach the sliding surface with an exponential policy. The proposed SMC has a simple structure because it is derived from the associated first-order differential equation and is capable of handling system disturbances and nonlinearities. The effectiveness of the proposed control method is validated using intensive simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 117–124, 2016

]]>In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic Lü system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 125–130, 2016

]]>Synchronization and control of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this article, we investigate the problem of impulsive synchronization for the complex-variable delayed chaotic systems with parameters perturbation and unknown parameters in which the time delay is also included in the impulsive moment. Based on the theories of adaptive control and impulsive control, synchronization schemes are designed to make a class of complex-variable chaotic delayed systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Sufficient conditions are derived to synchronize the complex-variable chaotic systems include delayed impulses. To illustrate the effectiveness of the proposed schemes, several numerical examples are given. © 2014 Wiley Periodicals, Inc. Complexity 21: 131–142, 2016

]]>This article is concerned with the asymptotic stability analysis of Takagi–Sugeno stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed time-varying delays. Based on the Lyapunov functional and linear matrix inequality (LMI) technique, sufficient conditions are derived to ensure the global convergence of the equilibrium point. The proposed conditions can be checked easily by LMI Control Toolbox in Matlab. It has been shown that the results are less restrictive than previously known criteria. They are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. Numerical examples are given to demonstrate the effectiveness of our results. © 2014 Wiley Periodicals, Inc. Complexity 21: 143–154, 2016

]]>The solution to the game of Lights Out and its many variants have been well studied. This article introduces Langton's turmite to the game of Lights Out and discusses when Langton's turmite can solve Lights Out on a torus. The article also explores the behavior of multiple Langton's turmites on a Lights Out on a torus. © 2014 Wiley Periodicals, Inc. Complexity 21: 155–161, 2016

]]>*Slime mould* Physarum polycephalum *is a single cell visible by an unaided eye. The slime mould optimizes its network of protoplasmic tubes in gradients of attractants and repellents. This behavior is interpreted as computation. Several prototypes of the slime mould computers were designed to solve problems of computation geometry, graphs, transport networks, and to implement universal computing circuits. Being a living substrate, the slime mould does not halt its behavior when a task is solved but often continues foraging the space thus masking the solution found. We propose to use temporal changes in compressibility of the slime mould patterns as indicators of the halting of the computation. Compressibility of a pattern characterizes the pattern's morphological diversity, that is, a number of different local configurations. At the beginning of computation the slime explores the space, thus generating less compressible patterns. After gradients of attractants and repellents are detected the slime spans data sites with its protoplasmic network and retracts scouting branches, thus generating more compressible patterns. We analyze the feasibility of the approach on results of laboratory experiments and computer modelling*. © 2015 Wiley Periodicals, Inc. Complexity 21: 162–175, 2016

Modularity is a natural instrument and a ubiquitous practice for the engineering of human-made systems. However, modularization remains more of an art than a science; to the extent that the notion of optimal modularity is rarely used in engineering design. We prove that optimal modularity exists (at least for construction)—and is achieved through balanced modularization as structural symmetry in the distribution of the sizes of modules. We show that system construction cost is highly sensitive to both the number of modules and the modularization structure. However, this sensitivity has an inverse relationship with process capability and is minimal for highly capable construction processes with small process uncertainties. Conclusions are reached by a Bayesian estimation technique for a relatively simple construction model originally introduced by Herbert Simon for the hypothetical production of a linear structure, taking into account errors that may occur in the work associated with the production of the links between the nodes in the structure for varied numbers of modules. © 2015 Wiley Periodicals, Inc. Complexity 21: 176–189, 2016

]]>In this article, the mean square exponential synchronization of a class of impulsive coupled neural networks with time-varying delays and stochastic disturbances is investigated. The information transmission among the systems can be directed and lagged, that is, the coupling matrices are not needed to be symmetrical and there exist interconnection delays. The dynamical behaviors of the networks can be both continuous and discrete. Specially, the time-varying delays are taken into consideration to describe the impulsive effects of the system. The control objective is that the trajectories of the salve system by designing suitable control schemes track the trajectories of the master system with impulsive effects. Consequently, sufficient criteria for guaranteeing the mean square exponential convergence of the two systems are obtained in view of Lyapunov stability theory, comparison principle, and mathematical induction. Finally, a numerical simulation is presented to show the verification of the main results in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 190–202, 2016

]]>This article presents a new design of robust finite-time controller which replaces the traditional automatic voltage regulator for excitation control of the third-order model synchronous generator connected to an infinite bus. The effects of system uncertainties and external noises are fully taken into account. Then a single input robust controller is proposed to regulate the system states to reach the origin in a given finite time. The designed robust finite-time excitation controller can refine the system behaviors in convergence and robustness against model uncertainties and external disturbances. The robustness and finite-time stability of the closed-loop system are analytically proved using the finite-time control idea and Lyapunov stability theorem. The suitability and robustness of the designed controller are shown in contrast with two other strong nonlinear control strategies. The main advantages of the proposed controller are as follows: a) robustness against system uncertainties and external noises; b) convergence to the equilibrium point in a given finite time; and c) the use of a single control input. © 2015 Wiley Periodicals, Inc. Complexity 21: 203–213, 2016

]]>In this article, the robust state estimation problem for Markov jump genetic regulatory networks (GRNs) based on passivity theory is investigated. Moreover, the effect of time-varying delays is taken into account. The focus is on designing a linear state estimator to estimate the concentrations of the mRNAs and the proteins of the GRNs, such that the dynamics of the state estimation error can be stochastically stable while achieving the prescribed passivity performance. By applying the Lyapunov–Krasovskii functional method, delay-dependent criteria are established to ensure the existence of the mode-dependent estimator in the form of linear matrix inequalities. Based on the obtained results, the parameters of the desired estimator gains can be further calculated. Finally, a numerical example is given to illustrate the effectiveness of our proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 214–223, 2016

]]>This article investigates the robust reliable control problem for a class of uncertain switched neutral systems with mixed interval time-varying delays. The system under study involves state time-delay, parameter uncertainties and possible actuator failures. In particular, the parameter uncertainties is assumed to satisfy linear fractional transformation formulation and the involved state delay are assumed to be randomly time varying which is modeled by introducing Bernoulli distributed sequences. The main objective of this article is to obtain robust reliable feedback controller design to achieve the exponential stability of the closed-loop system in the presence of for all admissible parameter uncertainties. The proposed results not only applicable for the normal operating case of the system, but also in the presence of certain actuator failures. By constructing an appropriate Lyapunov–Krasovskii functional, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched neutral system. More precisely, zero inequality approach, Wirtinger's based inequality, convex combination technique and average dwell time approach are used to simplify the derivation in the main results. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the proposed design approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–237, 2016

]]>The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. For any integer t≥1, a graph G is called t-apex tree if there exists a t-set such that G − X is a tree, while for any with , G − Y is not a tree. Let be the set of t-apex trees of order n. In this article, we determine the extremal graphs from with minimal and maximal matching energies, respectively. Moreover, as an application, the extremal cacti of order n and with s cycles have been completely characterized at which the minimal matching energy are attained. © 2015 Wiley Periodicals, Inc. Complexity 21: 238–247, 2016

]]>This article presents the robust dissipativity and passivity analysis of neutral-type neural networks with leakage time-varying delay via delay decomposition approach. Using delay decomposition technique, new delay-dependent criteria ensuring the considered system to be -γ dissipative are established in terms of strict linear matrix inequalities. A new Lyapunov–Krasovskii functional is constructed by dividing the discrete and neutral delay intervals into m and l segments, respectively, and choosing different Lyapunov functionals to different segments. Further, the dissipativity behaviors of neural networks which are affected due to the sensitiveness of the time delay in the leakage term have been taken into account. Finally, numerical examples are provided to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 248–264, 2016

]]>This article investigates the problem of output tracking control for a class of discrete-time interval type-2 (IT2) fuzzy systems subject to mismatched premise variables. Based on the IT2 Takagi–Sugeno (T–S) fuzzy model, the criterion to design the desired controller is obtained, which guarantees the closed-loop system to be asymptotically stable and satisfies the predefined cost function. Moreover, the controller to be designed does not need to share the same premise variables of the system, which enhances the flexibility of controller design and reduces the conservativeness. Finally, two examples are provided to demonstrate the effectiveness of the method proposed in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 265–276, 2016

]]>On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval-valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval-valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval-valued intuitionistic fuzzy generalized weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016

]]>The problem of stabilization for wireless networked control system (NCS) with packet dropout and time delay is studied in this article. The impulsive control law for the NCS is defined with time delay and impulse. Using a switching model, the network-induced imperfections can be treated as three switching subsystems. Therein, in the case of packet dropout, the control law use the previous state via the first-order hold. The impulsive control law is designed using the switched system approach and the average dwell time method. The obtained sufficient conditions which can guarantee the exponential stability of switched system are in the form of linear matrix inequalities. Finally, a numerical example is used to demonstrate the merits and applicabilities of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 291–299, 2016

]]>We aimed to evaluate the novel chaotic global techniques of heart rate variability (HRV) analysis during a specific autonomic test, the mental arithmetic overload test. These are spectral detrended fluctuation analysis and spectral multi-taper method; in addition to spectral entropy. We analyzed 24 healthy male students—all nonsmokers, aged between 18 and 22 years old. HRV was analyzed in the following periods: control protocol—the 10-min periods before the performance of the task and the 5-min periods during the performance of the test. Following tests for normality; Kruskal–Wallis technique and principal component analysis—it was decided that this type of mental stimulation did not lead to significant changes in any of the seven combinations of chaotic globals. In conclusion, it was suggested that the time-series be increased to 1000 RR intervals (at least 20 min of electrocardiographic data) and standard nonlinear methods be introduced in combination with spectral factors as a way of increasing the statistical significance. © 2015 Wiley Periodicals, Inc. Complexity 21: 300–307, 2016

]]>This article focuses on the robust sampled-data control for a class of uncertain switched neutral systems based on the average dwell-time approach. In particular, the system is considered with probabilistic input delay using sampled state vectors, which are described by the stochastic variables with a Bernoulli distributed white sequence and time-varying norm-bounded uncertainties. By constructing a novel Lyapunov–Krasovskii functional which involves the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities for ensuring the robust exponential stability of the uncertain switched neutral system about its equilibrium point. Moreover, based on the stability criteria, a state feedback sampled-data control law is designed for the considered system. Finally, a numerical example based on the water-quality dynamic model for the Nile River is given to illustrate the effectiveness of the proposed design technique. © 2015 Wiley Periodicals, Inc. Complexity 21: 308–318, 2016

]]>This article is concerned with master–slave synchronization for two chaotic Hindmarsh–Rose neurons. The main contribution of this article is that three synchronization criteria are derived by using linear feedback control without the estimation of bounds of state variables of controlled slave neurons. Three simulation examples are used to illustrate the effectiveness of our results. © 2015 Wiley Periodicals, Inc. Complexity 21: 319–327, 2016

]]>Self-organising traffic lights (SOTL) are considered a promising instrument for the development of more efficient adaptive traffic control systems. In this paper, we explain why this technology should be scrutinised and carefully reviewed. Research projects based on SOTL currently under way should be reviewed too. © 2015 Wiley Periodicals, Inc. Complexity 21: 328–330, 2016

]]>Previous work has shown that mutation bias can direct evolutionary trends in genotypic space under strong selection and rare mutation. We present an extension of this work to general traits of the organism. We do this by allowing many different genotypes, with different fitnesses, to have the same trait value. This approach makes novel predictions and shows that the outcome of evolution for a trait is influenced by mutation bias as well as the fitness distribution of the genotypes that have the same trait value. This distribution can alter evolution in interesting ways, depending on the likelihood of generating high fitness mutants. We also show that mutation bias can direct evolution when many mutants are present at any one time. We demonstrate that mutation bias can drive long-term evolutionary trends when the environment is constantly changing. Under biologically realistic conditions, we show that mutation bias can counter strong gradients of environmental selection over time. We conclude that evolutionary trends can be quite independent of the environment, even when they depress population fitness. Finally, we show that entropy can be a powerful source of mutation bias and can drive evolutionary trends. © 2015 Wiley Periodicals, Inc. Complexity 21: 331–345, 2016

]]>This article deals with a bioeconomic model of prey–predator system with Holling type III functional response. The dynamical behavior of the system is extensively discussed. Continuous type gestational delay of predators is incorporated in the system to study delay induced instability. It is observed that the system undergoes singularity induced bifurcation at interior equilibrium point when net economic revenue of the system increases through zero. State feedback controller is designed to stabilize the system at positive economic profit. Time delay is considered as a bifurcation parameter to prove the occurrence of Hopf bifurcation phenomenon in the neighborhood of the coexisting equilibrium point. Finally, some numerical simulations are carried out to verify the analytical results and the system is analyzed through graphical illustrations. © 2015 Wiley Periodicals, Inc. Complexity 21: 346–360, 2016

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