Synchronization of delayed complex dynamical networks with impulsive and stochastic effects

In this paper, the globally exponential synchronization of delayed complex dynamical networks with impulsive and stochastic perturbations is studied. The concept named “average impulsive interval” with “elasticity number” of impulsive sequence is introduced to get a less conservative synchronization criterion. By comparing with existing results, in which maximum or minimum of impulsive intervals are used to derive the synchronization criterion, the proposed synchronization criterion increases (or decreases) the impulse distances, which leads to the reduction of the control cost (or enhance the robustness of anti-interference) as the most important characteristic of impulsive synchronization techniques. It is discovered in our criterion that “elasticity number” has influence on synchronization of delayed complex dynamical networks but has no influence on that of non-delayed complex dynamical networks. Numerical simulations including a small-world network coupled with delayed Chua’s circuit are given to show the effectiveness and less conservativeness of the theoretical results.     

Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays

This paper considers the chaotic synchronization problem of neural networks with time-varying and distributed delays using impulsive control method. By utilizing the stability theory for impulsive functional differential equations, several impulsive control laws are derived to guarantee the exponential synchronization of neural networks with time-varying and distributed delays. It is shown that chaotic synchronization of the networks is heavily dependent on the designed impulsive controllers. Moreover, these conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. Finally, a numerical example and its simulation are given to show the effectiveness and advantage of the proposed control schemes.     

A new impulsive synchronization criterion for T–S fuzzy model and its applications

This paper focuses on the problem of impulsive synchronization of T–S fuzzy systems. A new synchronization criterion is derived for T–S fuzzy systems by utilizing the concept of average impulsive interval. The proposed impulsive control scheme has a simple control structure, and is theoretically and numerically proved to be less conservative than some existing results. The method is also illustrated by applying to Lorenz system, Rössler’s system as well as permanent magnet synchronous motors system.     

Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays

This paper presents a general impulsively-coupled complex switched network (ICCSN) model with parametric uncertainties and multiple Time-varying Delays in both the linear and nonlinear terms. The model is more general than those in the literature in that it contains switching behaviors on nodes and impulsive effects in the whole topology. Robust synchronization of ICCSNs with parametric uncertainties and time-varying delays is investigated. Based on the Lyapunov stability theory, delay-independent synchronization conditions for ICCSNs with uncertainties and delays are obtained. In addition, we consider five special synchronization cases: ICCSNs with delays in both the linear and nonlinear terms, ICCSNs with parametric uncertainties and delays either in the linear or in the nonlinear term, ICCSNs without switching behaviors but with parametric uncertainties and delays, and impulsively-switched-coupled complex switched network with uncertainties and delays. A systematic-design procedure is presented, and a numerical example is carried out to demonstrate the effectiveness of the proposed synchronization strategy. A comparative study of the maximum impulsive intervals for synchronization is presented for all special cases.     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations

In this paper, we study the exponential synchronization problem of a class of chaotic delayed neural networks with impulsive and stochastic perturbations. The involved time delays include time-varying delays and unbounded distributed delays. Employing the method of impulsive delay differential inequality, several new sufficient conditions ensuring the exponential synchronization are obtained, which can be easily checked by LMI Control Toolbox in Matlab. Compared with the previous methods, our method does not resort to complicated Lyapunov–Krasovkii, and the results derived are independent of the time-varying delays and do not require the differentiability of delay functions and the monotony of the activation functions. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained results in this paper.     

Network synchronization under distributed delayed impulsive control: Average delayed impulsive weight approach

This paper mainly investigates synchronization of complex dynamical networks (CDNs) with both system delay and coupled delay through distributed delayed impulsive control. Instead of constraining the impulsive weight and impulsive delay one by one, a new concept of average delayed impulsive weight is proposed to obtain more relaxed conditions. Subsequently, based on the impulsive control topology, Lyapunov theory and linear matrix inequality (LMI) design, certain flexible criteria of global exponential synchronization (GES) are given and the corresponding convergence rate is estimated. It is interesting to see that the CDNs can still achieve synchronization under comprehensive conditions though impulsive weights work negatively. Namely, the delays in impulsive control are able to promote synchronization potentially. Finally, simulations are given to show that the distributed delayed impulsive control can not only speeds up the convergence rate for synchronized networks, but also facilitates synchronization for desynchronized networks. In addition, the obtained results can be applied to unmanned craft systems.     

Impulsive synchronization of time-varying dynamical network

Synchronization of time-varying dynamical network is investigated via impulsive control. Based on the Lyapunov function method and stability theory of impulsive differential equation, a synchronization criterion with respect to the system parameters and the impulsive gains and intervals is analytically derived. Further, an adaptive strategy is introduced for designing unified impulsive controllers, with a corresponding synchronization criterion derived. In this proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is provided and evaluated. The derived theoretical results are illustrated to be effective by several numerical examples.     

Dynamical analysis of impulsive neural networks with time‐varying delays

In this work, a new criterion concerning the global exponential stability of impulsive neural networks with time‐varying delays is presented by employing the impulsive delayed differential inequality method. The criterion is independent of the time‐varying delays and does not require the differentiability of delay functions. An example and its simulation showing the effectiveness of the present criterion is given finally. Copyright © 2012 John Wiley & Sons, Ltd.     

Permanence for General Nonautonomous Impulsive Population Systems of Functional Differential Equations and Its Applications

In this paper, we investigate general impulsive nonautonomous population dynamical systems of functional differential equations. By utilizing the method of multiple Liapunov-like functionals to construct the permanence region, a general criterion on the permanence for the system is established. Furthermore, as applications of this general criterion, a class of impulsive nonautonomous n-species Lotka–Volterra competitive systems with delays and a class of impulsive nonautonomous 3-species Lotka–Volterra food chain systems with delays are discussed. Some new and useful sufficient conditions on the permanence for these systems are established.     

Lag synchronization of structurally nonequivalent chaotic systems with time delays

In this paper, we investigate the synchronization of a class of structurally nonequivalent chaotic systems with time delays. The nonequivalence could be parameter mismatches, differences in the time delays or more complicated nonequivalent structures. We give a unified approach, via unidirectional and impulsive control, to them achieving lag synchronization. Then we apply this method to typical time-delay chaotic systems: Mackey–Glass and Ikeda models. The corresponding estimations are given. Lastly, we compare the results with existing results.     

Further analysis on uniform stability of impulsive infinite delay differential equations

A criterion for the uniform stability of impulsive functional differential equations with infinite delays is presented by using Lyapunov functions and the Razumikhin technique. The criterion is more general than several recent works. An example showing the effectiveness and advantage of the present criterion is given.     

具概率延迟反馈金融系统的脉冲控制

研究了概率时滞脉冲金融系统平衡点的全局渐近稳定性问题。首先,通过定义合适的时滞分段区间上的随机变量,给出了概率时滞的脉冲金融系统的数学模型,根据脉冲微分不等式特点构造了一个简便合适的Lyapunov函数利用脉冲微分不等式引理、控制脉冲间隔与脉冲量以及概率时滞分析技巧,获得了较大时滞允许范畴下的平衡点的全局指数稳定,并通过数值实例验证了方法的可行性以及概率时滞的优势。特别地,稳定性判定准则的时滞允许上限的增大,扩大了准则的实用性.     

Feedback control based on discrete-time state observations on synchronization of stochastic impulsive coupled systems

In this paper, feedback control based on discrete-time state observations is used to study the inner synchronization of stochastic impulsive coupled systems (SICSs). Therein, the coupling strength of SICSs is state-dependent switching and time-varying under each switching. Besides, by means of average impulsive interval approach, the Lyapunov method and the graph theory, a synchronization criterion of SICSs is presented. As an application, stochastic impulsive coupled Chua’s circuits with state-dependent switching coupling strength are investigated for the first time and some sufficient conditions are given. Finally, in order to illustrate the effectiveness of our main results, some numerical simulations are presented.     

Synchronization of quaternion-valued coupled systems with time-varying coupling via event-triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion-valued and time-varying, which makes our model more in line with practical models. First, we prove that event-triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion-valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion-valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.     

具有时滞和脉冲的非线性食饵-竞争系统的正周期解

利用重合度理论中的延拓定理研究了脉冲作用对非线性时滞食饵-竞争系统的影响,即考察具有时滞和脉冲的非线性食饵-竞争系统的周期性,得到了该系统存在非平凡正周期解的一个充分性判别依据.     

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     

基于事件触发控制带有多时变时滞的主从系统同步

研究了基于事件触发机制下带有多个时变时滞的主从系统同步问题.事件触发机制的提出,使得在实现主从系统同步的过程中,可以有效降低数据传输量,减轻网络带宽的压力.通过Lyapunov稳定理论和线性矩阵不等式的方法,得到了带有多时变时滞的主从系统同步的充分条件.最后,通过MATLAB仿真,验证了所提出同步准则的有效性.     

A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays

This paper considers the global exponential stability and exponential convergence rate of impulsive neural networks with continuously distributed delays in which the state variables on the impulses are related to the unbounded distributed delays. By establishing a new impulsive delay differential inequality, a new criterion concerning global exponential stability for these networks is derived, and the estimated exponential convergence rate is also obtained. The result extends and improves on earlier publications. In addition, two numerical examples are given to illustrate the applicability of the result. Copyright © 2010 John Wiley & Sons, Ltd.     

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.