Modeling networked systems using the topologically distributed bounded rationality framework

In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer‐to‐peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real‐world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game‐theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer‐to‐peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer‐to‐peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 123–137, 2016     

Robust state estimation for Markov jump genetic regulatory networks based on passivity theory

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     

Statistically q‐deformed and tau‐deformed systems

Two classes of statistically deformed systems are known in literature. They are, respectively, the q‐deformed systems (Lavagno and Narayana Swamy, Phys Rev E 2002, 65, 036101) and the κ‐deformed systems (Kaniadakis and Scarfone, Physica A 2002, 305, 69). In this article, a new class, i.e., the tau‐deformed systems, is introduced. For each of these systems, a consistent thermodynamics may be developed. A summary of the main similarities between the thermodynamic properties of q‐deformed and tau‐deformed systems is presented. The deformation outlined in this article is radically different from the nonextensive Tsallis statistics, where the structure of the entropy is rather arbitrary deformed via the logarithmic function. In contrast, the theory of tau‐deformed systems is developed on a purely physical basis. However, one finally shows that the tau‐systems may be described by using a new form of deformed logarithmic function. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Mean square exponential synchronization for impulsive coupled neural networks with time‐varying delays and stochastic disturbances

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     

A BRIEF INTRODUCTION TO SCALE‐FREE NETWORKS

ABSTRACT. This article provides a brief introduction to scale‐free networks. The notion of a scale‐free network is defined and some examples given. Properties frequently exhibited by scale‐free networks are discussed. The importance of the phenomenon of preferential attachment in generating scale‐free networks is illustrated with two examples for the spread of a persistent disease. The models are similar in that they both yield a total infected population (1) which is geometrically distributed, and growing exponentially in expectation; and (2) in which the average distance from the original source of infection grows in a similar way over time. However one model, which has preferential attachment (infection), yields a scale‐free network, while the other which has homogeneous infectivity does not. The possible application of the theory of scale‐free networks to resource management is briefly discussed.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

Teaching complexity theory through student construction of a course wiki: The self‐organization of a scale‐free network

Complex systems are fascinating because emergent phenomena are often unpredictable and appear to arise ex nihilo. The other side of this fascination, however, is a certain difficulty in comprehending complex systems, particularly for students. To help students more fully understand emergence and self‐organization, a course on complexity theory was designed to not only be about these two concepts, but itself embody them. The principal design tool was a course wiki. Here, we quantitatively demonstrate that this course wiki self‐organized into a scale‐free network. This is particularly notable given the small size of the network. We conclude by noting a few qualitative examples of emergence, as well as offering recommendations for the future use of wikis in teaching complexity theory. © 2010 Wiley Periodicals, Inc. Complexity 16: 41–48, 2011     

A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems

This article reports a numerical discretization scheme, based on two‐dimensional integrated radial‐basis‐function networks (2D‐IRBFNs) and rectangular grids, for solving second‐order elliptic partial differential equations defined on 2D nonrectangular domains. Unlike finite‐difference and 1D‐IRBFN Cartesian‐grid techniques, the present discretization method is based on an approximation scheme that allows the field variable and its derivatives to be evaluated anywhere within the domain and on the boundaries, regardless of the shape of the problem domain. We discuss the following two particular strengths, which the proposed Cartesian‐grid‐based procedure possesses, namely (i) the implementation of Neumann boundary conditions on irregular boundaries and (ii) the use of high‐order integration schemes to evaluate flux integrals arising from a control‐volume discretization on irregular domains. A new preconditioning scheme is suggested to improve the 2D‐IRBFN matrix condition number. Good accuracy and high‐order convergence solutions are obtained. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Quantized control for polynomial fuzzy discrete‐time systems

This article investigates the control problem for polynomial fuzzy discrete‐time systems. Signal quantization is considered in this article. To deal with this issue, a logarithmic quantizer is adopted to quantize the control signal. First, a novel method is first proposed to model polynomial fuzzy discrete‐time systems and handle the quantized control problem of the systems. Second, based on Lyapunov‐stability theory, sufficient conditions are obtained in terms of sum of squares to guarantee the asymptotical stability of the systems and satisfy a performance. Finally, a simulation example is given to illustrate the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 325–332, 2015     

Global lagrange stability of complex‐valued neural networks of neutral type with time‐varying delays

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

Synchronization of delayed coupled reaction‐diffusion systems on networks

In this paper, the exponential synchronization problem of delayed coupled reaction‐diffusion systems on networks (DCRDSNs) is investigated. Based on graph theory, a systematic method is designed to achieve exponential synchronization between two DCRDSNs by constructing a global Lyapunov function for error system. Two different kinds of sufficient synchronization criteria are derived in the form of Lyapunov functions and coefficients of drive‐response systems, respectively. Finally, a numerical example is given to show the usefulness of the proposed criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus protocol design for discrete‐time networks of multiagent with time‐varying delay via logarithmic quantizer

This article considers the problem of consensus for discrete‐time networks of multiagent with time‐varying delays and quantization. It is assumed that the logarithmic quantizer is utilized between the information flow through the sensor of each agent, and its quantization error is included in the proposed method. By constructing a suitable Lyapunov‐Krasovskii functional and utilizing matrix theory, a new consensus criterion for the concerned systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Based on the consensus criterion, a designing method of consensus protocol is introduced. One numerical example is given to illustrate the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 163–176, 2015     

Finite‐time stability of fractional‐order stochastic singular systems with time delay and white noise

In this article, the finite‐time stochastic stability of fractional‐order singular systems with time delay and white noise is investigated. First the existence and uniqueness of solution for the considered system is derived using the basic fractional calculus theory. Then based on the Gronwall's approach and stochastic analysis technique, the sufficient condition for the finite‐time stability criterion is developed. Finally, a numerical example is presented to verify the obtained theory. © 2016 Wiley Periodicals, Inc. Complexity 21: 370–379, 2016     

Signal moments for the short‐time Fourier transform associated with Hardy–Sobolev derivatives

The short‐time Fourier transform has been shown to be a powerful tool for non‐stationary signals and time‐varying systems. This paper investigates the signal moments in the Hardy–Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non‐smooth signals if we replace the classical derivatives by the Hardy–Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short‐time Fourier domain are established in the Hardy–Sobolev space. Copyright © 2014 John Wiley & Sons, Ltd.     

Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

The concept of mono‐component is widely used in nonstationary signal processing and time‐frequency analysis. In this paper, we construct several classes of complete rational function systems in the Hardy space, whose boundary values are mono‐components. Then, we propose a best approximation algorithm (BAA) based on optimal selections of two parameters in the orthonormal bases according to the approximation error. Effectiveness of BAA is evaluated by comparison experiments with the classical Fourier decomposition algorithm. It is also shown that BAA has promising results for filtering out noises and dealing with real‐world signals. Copyright © 2014 John Wiley & Sons, Ltd.     

An efficient forward–reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

In this work, we present an extension of the forward–reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994–2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the expectation-maximization algorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.     

A graph‐theoretic method to stabilize the delayed coupled systems on networks based on periodically intermittent control

This paper mainly focus on the exponential stabilization problem of coupled systems on networks with mixed time‐varying delays. Periodically intermittent control is used to control the coupled systems on networks with mixed time‐varying delays. Moreover, based on the graph theory and Lyapunov method, two different kinds of stabilization criteria are derived, which are in the form of Lyapunov‐type theorem and coefficients‐type criterion, respectively. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, a decision theorem is also presented. It is straightforward to show the stability of original system can be determined by that of modified system with added absolute value into the coupling weighted‐value matrix. Finally, the feasibility and validity of the obtained results are demonstrated by several numerical simulation figures.     

A cellular automata model can quickly approximate UDP and TCP network traffic

Brooks and Orr [R.R. Brooks and N. Orr, A model for mobile code using interacting automata. IEEE Trans Mobile Computing 2002, 1(4)] present a model for analysis and simulation of mobile code systems based on cellular automata (CA) abstractions. One flaw with that article was a lack of experimental support showing that CA can model IP networks. This article presents CA models, consistent with those in the work of Brooks and Orr, that model the transport layer of IP networks. We show how these models may be generalized for more complicated network topologies. We provide quantitative results comparing the quality of our CA implementation versus the standard network modeling tool ns‐2. The results from the CA model are qualitatively similar to ns‐2, but the CA simulation runs significantly faster and scales better. © 2004 Wiley Periodicals, Inc. Complexity 9:32–40, 2004