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 presents new theoretical results on the synchronization for a class of fractional-order delayed neural networks with hybrid coupling that contains constant coupling and discrete-delay coupling. This is the first attempt to investigate the synchronization problem of fractional-order coupled delayed neural networks. Based on the fractional-order Lyapunov stability theorem and Kronecker product properties, sufficient criteria are established to ensure the fractional-order coupled neural network to achieve synchronization. Numerical simulations are given to illustrate the correctness of the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>A hybrid technique for solving the congestion management problem in an electricity market based on harmony search algorithm (HAS) and Fuzzy mechanism is presented in this article. This algorithm does not require initial value setting for the variables and does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. The HAS is a recently developed powerful evolutionary algorithm, inspired by the improvisation process of musicians, for solving single/multiobjective optimization problems. In the proposed technique, each musician plays a note for finding a best harmony all together. Transmission pricing and congestion management are the key elements of a competitive electricity market based on direct access. They also focus of much of the debate concerning alternative approaches to the market design and the implementation of a common carrier electricity system. This article focuses on the tradeoffs between simplicity and economic efficiency in meeting the objectives of a transmission pricing and congestion management scheme. The effectiveness of the proposed technique is applied on 30 and 118 bus IEEE standard power system in comparison with CPSO, PSO-TVAC, and PSO-TVIW. The numerical results demonstrate that the proposed technique is better and superior than other compared methods. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>In this article, the dynamical behavior of a generalized Lorenz system is derived based on stability theory of dynamical systems. The meaningful contribution of this article is that the domain of attraction of the new chaotic system is studied in detailed. Finally, numerical simulations are given to verify the effectiveness and correctness of the obtained results. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This article is concerned with the nonfragile filtering for wireless-networked systems with energy constraint. To achieve the energy-efficient goal, the local measurement is first sampled by nonuniform sampling, then we only choose one measurement to transmit it to the remote filter. In the filter design, the random occurring filter gain variation problem is taken into account. A new stochastic switched system model is presented to capture the nonuniform sampling, the measurement size reduction, and the random filter gain phenomena. Based on the switched system approach, stochastic system analysis, and Lyapunov stability theory, a sufficient condition is presented such that the filtering error system is exponentially stable in the mean-square sense and a prescribed performance level is also guaranteed. The effectiveness of the proposed new method is illustrated by a simulation example. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>The idea of emergence originates from the fact that global effects emerge from local interactions producing a collective coherent behavior. A particular instance of emergence is illustrated by a flocking model of interacting “boids” encompassing two antagonistic conducts—consensus and frustration—giving rise to highly complex, unpredictable, coherent behavior. The cohesive motion arising from consensus can be described in terms of three ordered dynamic phases. Once frustration is included in the model, local phases for specific groups of flockmates, and transitions among them, replace the global ordered phases. Following the evolution of boids in a single group, we discovered that the boids in this group will alternate among the three phases. When we compare two uncorrelated groups, the second group shows a similar behavior to the first one, but with a different sequence of phases. Besides the visual observation of our animations with marked boids, the result is evident plotting the local order parameters. Rather than adopting one of the consensus ordered phases, the flock motion resembles more an entangled dynamic sequence of phase transitions involving each group of flockmates. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>The authors consider the Orthodox iconography of Byzantine style aimed at examining the existence of complex behavior and fractal patterns. It has been demonstrated that fractality in icons is manifested as two types—descending and ascending, where the former one corresponds to the apparent information and the latter one to the hidden causal information defining the spatiality of icon. Self-organization, recognized as the increase of the causal information in temporal domain, corresponds to contextualization of the observer's personage position. The results presented in the forms of plots and tables confirm the adequacy of the model being the completion of visual perception. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>An agent-based model is constructed to study the effects of individual irrationality and network structure on collective performance. We find that individual irrationality and network density are the most influential factors. Moderate degree of irrationality results in moderate knowledge unity and superior quality of knowledge; increasing network connections or decreasing average path length (APL) can promote quality of knowledge integration and knowledge unity. Furthermore, APL is more influential than clustering coefficient and centralization (CE). Less clustering may contribute to higher quality of knowledge integration, while higher CE may contribute to higher knowledge unity. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>The dynamics of a reaction-diffusion predator-prey model with hyperbolic mortality and Holling type II response effect is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system which are spatially homogeneous. To verify our theoretical results, some numerical simulations are also presented. © 2015 Wiley Periodicals, Inc. Complexity, 2015

]]>This article addresses stability analysis of a general class of memristor-based complex-valued recurrent neural networks (MCVNNs) with time delays. Some sufficient conditions to guarantee the boundedness on a compact set that globally attracts all trajectories of the MCVNNs are obtained by utilizing local inhibition. Moreover, some sufficient conditions for exponential stability and the global stability of the MCVNNs are established with the help of local invariant sets and linear matrix inequalities using Lyapunov–Krasovskii functional. The analysis results in the article, based on the results from the theory of differential equations with discontinuous right-hand sides as introduced by Filippov. Finally, two numerical examples are also presented to show the effectiveness and usefulness of our theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–39, 2016

]]>This article presents a new approach to economic load dispatch (ELD) problems by the considering the cost functions, impact renewable energy as wind turbin and subsidies. Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to meet the system load, at the lowest possible cost, subject to transmission and operational constraints. The main goal in the deregulated system is subsidies and analysis performance on government to minimize the total fuel cost while satisfying the load demand and operational constraints. The practical ELD problems have nonsmooth cost functions with equality and inequality constraints, which make the problem of finding the global optimum difficult when using any mathematical approaches. Accordingly, particle swarm optimization with time-varying inertia weight (PSO-TVIW) used for solving this problem. The effectiveness of the proposed strategy is applied over real-world engineering problem and highly constrained. Obtained results indicate that PSO-TVIW can successfully solve this problem. © 2014 Wiley Periodicals, Inc. Complexity 21: 40–49, 2016

]]>A novel variable structure and disturbance rejection control strategy for a wind turbines equipped with a double fed induction generator based on stator-flux-oriented vector control is presented. According to estimation of maximum power operation points of wind turbine under stochastic wind velocity profiles and tracking them using traditional offline gain, scheduling and innovative adaptive online method is necessary. To demonstrate the effectiveness of the proposed control strategy, the estimation of maximum operating power point of wind turbine and tracking it under stochastic wind velocity profiles has been considered as a test case. Simulation results show the validity of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 50–62, 2016

]]>This manuscript analyzed the delay-dependent stability problem for non-linear switched singular time-delay systems based on average dwell time and delay decomposition approach. Both cases of time-delays namely constant and time-varying delays are treated in the switched singular systems. Based on piecewise Lyapunov–Krasovskii functional, linear matrix inequality technique and an average dwell time approach, sufficient conditions which ensures that the delay-dependent exponential stability conditions for uncertain switched singular systems are discussed. Finally, numerical examples and simulations are provided to demonstrate the effectiveness of the proposed techniques. © 2014 Wiley Periodicals, Inc. Complexity 21: 63–78, 2016

]]>This article is concerned with the boundedness solutions of the brushless DC motor system. For this system, the global attractive set and positively invariant set are obtained based on generalized Lyapunov function stability theory and the extremum principle of function. Furthermore, the rate of the trajectories is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 79–85, 2016

]]>We work on a model that has succeeded in describing real cases of coexistence of two languages within a closed community of speakers, taking into account bilingualism and incorporating a parameter to measure the distance between languages. The dynamics of this model depend on a characteristic exponent, which weighs the power of the size of a group of speakers to attract new members. So far, this model had been solved only when this characteristic exponent is greater than 1. In this article, we have managed to solve the nature of the stability of all the possible situations for this characteristic exponent, that is, when it is less or equal than 1 and covering also the situations produced when it is 0 or negative. We interpret these new situations and find that, even in such exotic scenarios, there are configurations of the resulting societies where all the languages coexist. © 2014 Wiley Periodicals, Inc. Complexity 21: 86–93, 2016

]]>