Defining synergy thermodynamically using quantitative measurements of entropy and free energy

Synergy is often defined as the creation of a whole that is greater than the sum of its parts. It is found at all levels of organization in physics, chemistry, biology, social sciences, and the arts. Synergy occurs in open irreversible thermodynamic systems making it difficult to quantify. Negative entropy or negentropy ( ) has been related to order and complexity, and so has work efficiency, information content, Gibbs Free Energy in equilibrium thermodynamics, and useful work efficiency in general ( ). To define synergy in thermodynamic terms, we use the quantitative estimates of changes in and in seven different systems that suffer process described as synergistic. The results show that synergistic processes are characterized by an increase in coupled to an increase in . Processes not associated to synergy show a different pattern. The opposite of synergy are dissipative processes such as combustion where both and decrease. The synergistic processes studied showed a relatively greater increase in compared to opening ways to quantify energy—or information—dissipation due to the second law of thermodynamics in open irreversible systems. As a result, we propose a precise thermodynamic definition of synergy and show the potential of thermodynamic measurements in identifying, classifying and analysing in detail synergistic processes. © 2016 Wiley Periodicals, Inc. Complexity 21: 235–242, 2016     

Fault‐tolerant mixed /passive synchronization for delayed chaotic neural networks with sampled‐data control

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

Scouting the Mandelbrot set with memory

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     

Fault‐tolerant sampled‐data mixed ℋ∞ and passivity control of stochastic systems and its application

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

Static output‐feedback control for interval type‐2 discrete‐time fuzzy systems

This article investigates the problem of reliable mixed control for discrete‐time interval type‐2 (IT2) fuzzy model‐based systems via static output‐feedback (SOF) control method. The number of fuzzy rules and the membership functions for the SOF controller are different from those for the plant. A sufficient criterion of reliable stability with mixed performance is derived for the closed‐loop system with sensor failure. The SOF controller is designed for two different cases (known sensor failure case and unknown sensor failure case) to guarantee the reliable stability with mixed performance. Moreover, novel criteria are presented to obtain the optical performance for the closed‐loop system. Finally, an example is used to verify the effectiveness of the proposed design scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 74–88, 2016     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015     

Decentralized Piecewise Fuzzy Output Feedback Control for Large‐Scale Nonlinear Systems with Time‐Varying Delay

This article addresses the decentralized output feedback control for discrete‐time large‐scale nonlinear systems. The considered large‐scale system contains several subsystems with nonlinear interconnection and time‐varying delay, and Takagi–Sugeno model is used to represent each nonlinear subsystem. We aim at designing a decentralized piecewise fuzzy memory dynamic‐output‐feedback (DOF) controller that guarantees the stabilization and performance of the resulting closed‐loop control system. First, we propose a model transformation that reformulates the problem of decentralized output feedback control into the stability analysis with input–output form. Then, we introduce a piecewise Lyapunov–Krasovskii functional, where all Lyapunov matrices are not necessarily positive definite. By combining with the scaled small gain theorem, the less conservative solution to the problem of decentralized piecewise fuzzy memory DOF controller design for the considered system is derived in terms of linear matrix inequalities. The advantage of the proposed method is finally validated using two numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 268–288, 2016     

synchronization of coupled reaction‐diffusion neural networks with mixed delays

The reaction‐diffusion neural network is often described by semilinear diffusion partial differential equation (PDE). This article focuses on the asymptotical synchronization and synchronization for coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. First, using the Lyapunov–Krasoviskii functional scheme, the sufficient condition is obtained for the asymptotical synchronization of coupled semilinear diffusion PDEs with mixed time‐delays and this condition is represented by linear matrix inequalities (LMIs), which is easy to be solved. Then the robust synchronization is considered in temporal‐spatial domain for the coupled semilinear diffusion PDEs with mixed delays and external disturbances. In terms of the technique of completing squares, the sufficient condition is obtained for the robust synchronization. Finally, a numerical example of coupled semilinear diffusion PDEs with mixed time‐delays is given to illustrate the correctness of the obtained results. © 2016 Wiley Periodicals, Inc. Complexity 21: 42–53, 2016     

H∞ stochastic synchronization for master–slave semi‐Markovian switching system via sliding mode control

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

Solitary wave solutions of coupled boussinesq equation

This article presents the general case‐study of our previous works regarding generalized Boussinesq equations [17, 18, 19], that focus on application of various subordinate methods where are applied to construct more general exact solutions of the coupled Boussinesq equations. In this article, the ‐expansion method is applied on coupled Boussinesq equations. Our work is motivated by the fact that the ‐expansion method provides not only more general forms of solutions but also periodic, solitary waves, and rational solutions. The method appears to be easier and faster by means of a symbolic manipulation program. © 2016 Wiley Periodicals, Inc. Complexity 21: 151–155, 2016     

Matching energy of unicyclic and bicyclic graphs with a given diameter

Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and be the roots of its matching polynomial. The ME of G is defined to be the sum of the absolute values of . In this article, we characterize the graphs with minimal ME among all unicyclic and bicyclic graphs with a given diameter d. © 2014 Wiley Periodicals, Inc. Complexity 21: 224–238, 2015     

Opinion dynamics with the contrarian deterministic effect and human mobility on lattice

Opinion dynamics under the influence of the contrarian deterministic effect and human mobility on the two‐dimensional lattice is studied. In the model, the opinion is a binary variable and some shortcuts are added with the adding probability P_s. At each time step, each agent with shortcuts is chosen as the mobile one with the mobility probability P_m and moves to one of his immobile neighbors along shortcuts randomly. Then, the immobile agents update their opinions based on the majority rule with p_f, which is the Fermi function of the interaction noise T due to the contrarian deterministic effect. We find that some appropriate interaction noise T enhances the formation of community around T_c. And human mobility enhances the formation of community when , where T_c is equal to the average degree and independent of the network size N and the mobility probability P_m through the theoretical and numerical analysis. Furthermore, we also find that the system with larger degree and the self‐feedback of agent have stronger robustness in the opinion formation with the contrarian deterministic effect. © 2014 Wiley Periodicals, Inc. Complexity 20: 43–49, 2015     

Nonfragile H∞ filtering for wireless‐networked systems with energy constraint

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 21: 79–89, 2016     

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     

Finite‐time l2 − l∞ synchronization for discrete‐time nonlinear chaotic systems via information‐constrained delayed feedback

This article is concerned with the problem of finite‐time synchronization control for a class of discrete‐time nonlinear chaotic systems under unreliable communication links. Our aim is to design a delayed feedback controller such that the resulting synchronization error system is stochastically finite‐time bounded with a guaranteed performance level over a finite time interval. Some sufficient conditions for the solvability of the above problem are established. A delayed feedback control scheme involving constrained information about the past state is presented. Finally, the Fold chaotic system is used to demonstrate the effectiveness of our proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 21: 138–146, 2015     

Linear‐Time Algorithms for Scattering Number and Hamilton‐Connectivity of Interval Graphs

We prove that for all an interval graph is ‐Hamilton‐connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best‐known time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k‐Hamilton‐connected can be computed in time.     

On centripetal flows of entities in scale‐free networks with nodes of finite capability

We examine the transmission of entities from the peripheries of scale‐free networks toward their centers when the nodes of the network have finite processing capabilities. We look at varying network utilization, U and find that clogging of the network sets in after a threshold value has been exceeded, and that the congestion sets in at the downstream nodes (those nearer to the collector) having large numbers of upstream neighbors. Investigation of the question of the degree of correlation of several characteristics of scale‐free networks (such as the average path length to the collector <l_(min)> and the average clustering coefficient ) with the dynamics of centripetal flow in them reveals a negative answer: any correlation is indirect and will manifest in the number of producer nodes (which dictate the effective heaviness of the flow) and the interconnectedness of the feeder nodes, those nodes which are immediate neighbors of the collector node. An examination of reinforcement strategies shows dramatic improvements in both the finishing rate, and the average total transmission time, when the more centrally‐placed nodes are reinforced first, showing that the entities spend a large amount of their lifetime waiting in line at those nodes (which constitute the bottlenecks in the network) compared to the nodes in the periphery. Our results reinforce the importance of a network's hubs and their immediate environs, and suggest strategies for prioritizing elements of a network for optimization. © 2014 Wiley Periodicals, Inc. Complexity 21: 283–295, 2015     

Robust reliable sampled‐data H∞ control for uncertain stochastic systems with random delay

In this article, the problem of robust reliable sampled‐data control for a class of uncertain nonlinear stochastic system with random delay control input against actuator failures has been studied. In the considered system, the parameter uncertainty satisfies the norm bounded condition and the involved time delay in control input are assumed to be randomly time‐varying which is modeled by introducing Bernoulli distributed sequences. By constructing a novel Lyapunov–Krasovskii functional involving with the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for ensuring the robust asymptotic stability of the uncertain nonlinear stochastic system with random delay and disturbance attenuation level about its equilibrium point for all possible actuator failures. In particular, Schur complement together with Jenson's integral inequality is utilized to substantially simplify the derivation in the main results. The derived analytic results are applied to design robust reliable sampled‐data controller for hanging crane structure model and simulation results are provided to demonstrate the effectiveness of the proposed control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 42–58, 2015     

The threshold for combs in random graphs

For let denote the tree consisting of an ‐vertex path with disjoint ‐vertex paths beginning at each of its vertices. An old conjecture says that for any the threshold for the random graph to contain is at . Here we verify this for with any fixed . In a companion paper, using very different methods, we treat the complementary range, proving the conjecture for (with ). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 794–802, 2016