Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes

This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.     

Impulsive synchronization seeking in general complex delayed dynamical networks

The present paper investigates the issues of impulsive synchronization seeking in general complex delayed dynamical networks with nonsymmetrical coupling. By establishing the extended Halanay differential inequality on impulsive delayed dynamical systems, some simple yet generic sufficient conditions for global exponential synchronization of the impulsive controlled delayed dynamical networks are derived analytically. Compared with some existing works, the distinctive features of these sufficient conditions indicate two aspects: on the one hand, these sufficient conditions can provide an effective impulsive control scheme to synchronize an arbitrary given delayed dynamical network to a desired synchronization state even if the original given network may be asynchronous itself. On the other hand, the controlled synchronization state can be selected as a weighted average of all the states in the network for the purpose of practical control strategy, which reveals the contributions and influences of various nodes in synchronization seeking processes of the dynamical networks. It is shown that impulses play an important role in making the delayed dynamical networks globally exponentially synchronized. Furthermore, the results are applied to a typical nearest-neighbor unidirectional time-delay coupled networks composed of chaotic FHN neuron oscillators, and numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.     

脉冲控制下复杂网络的同步

主要考虑非对称耦合复杂网络的脉冲同步问题.通过构造Lyapunov泛函,设计合适的脉冲控制器,并利用时滞脉冲系统理论,给出了网络脉冲同步新的判别准则.数值模拟表明所得结果是正确的.     

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.     

Further results on the impulsive synchronization of uncertain complex‐variable chaotic delayed systems

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

Single impulsive controller for globally exponential synchronization of dynamical networks

This paper is devoted to studying the synchronization control of impulsive dynamical networks. A single impulsive controller is proved to be effective for the stabilization of dynamical networks with impulse-coupling. Some simple and easily verified criteria are given for the stabilization of impulsive dynamical networks under a single impulsive controller and/or a single negative state-feedback control. Moreover, the effects of a single impulsive controller, a single state-feedback controller and an isolated dynamical system on the synchronization process are respectively distilled and explicitly expressed in the derived criteria. The structure of the dynamical network can be directed and weakly connected with a rooted spanning tree. Moreover, the convergence rate of the dynamical network is also explicitly estimated, and there is no requirement on the lower and upper bounds of the impulsive intervals. A numerical example is presented to illustrate the efficiency of the designed controller and the validity of the analytical results.     

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.     

New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling

The synchronization stability problem of general complex dynamical networks with non-delayed and delayed coupling is investigated based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of derivative of a Lyapunov functional in every subinterval, several new delay-dependent synchronization stability conditions are derived in the form of linear matrix inequalities, which are easy to be verified by the LMI toolbox. Some numerical examples show that, when the number of the divided subintervals increases, the corresponding criteria can provide much less conservative results.     

Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.     

Impulsive synchronization of general continuous and discrete-time complex dynamical networks

This paper mainly investigates the impulsive synchronization of a general complex continuous and discrete-time dynamical network. Firstly, for the continuous complex networks, we give a sufficient condition to guarantee its synchronization. When the sufficient condition is not satisfied, the impulsive controllers are utilized, and some novel criteria are derived to guarantee the network synchronization in this case. What is more significant is that the similar work is extended to the discrete-time networks model. Finally, the results are, respectively, illustrated by a continuous network composed with the chaotic Chen oscillators and a discrete-time network consisting of Hénon map. All numerical simulations verify the effectiveness of the theoretical analysis.     

Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method

In this paper, simple controllers are designed to realize the synchronization of complex networks with time delays, in which the coupling configuration matrix and inner coupling matrix are not restricted to be symmetric matrix. Several adaptive synchronization criteria are obtained based on Lyapunov stability theory. These criteria relay on the coupling strength and the number of nodes pinning to the networks. For a given complex dynamical network with both delayed and non-delayed couplings, we give the minimum number of controllers under which synchronization can be achieved. One example shows the effectiveness of the proposed pinning adaptive controller.     

Finite-time synchronization control of complex dynamical networks with time delay

In this paper, the finite-time synchronization between two complex networks with non-delayed and delayed coupling is proposed by using the impulsive control and the periodically intermittent control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. Especially, the traditional synchronization criteria are improved by using the impulsive control and the periodically intermittent control in the convergence time, the results of this paper are important. Finally, numerical examples are given to verify the effectiveness and correctness of the synchronization criteria.     

具有多重权值的时滞复杂网络固定时间同步问题研究

文章研究了基于非周期间歇性控制的具有多重权值和耦合时滞的复杂网络固定时间同步问题.通过构建具有多重权值的复杂网络模型,并基于固定时间稳定性引理和矩阵理论,给出了实现复杂网络固定时间同步的充分条件.此外,文章设计了固定时间非周期切换控制器,获得了实现复杂网络同步的时间上界的估计值.结论证明了实现网络同步的时间与网络的初始状态无关,最后数值模拟说明了理论结果的正确性和有效性.     

Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method

In this paper, an impulsive controller is designed to achieve the exponential synchronization of chaotic delayed neural networks with stochastic perturbation. By using the impulsive delay differential inequality technique that was established in recent publications, several sufficient conditions ensuring the exponential synchronization of chaotic delayed networks are derived, which can be easily checked by LMI Control Toolbox in Matlab. A numerical example and its simulation is given to demonstrate the effectiveness and advantage of the theory results.     

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.     

复杂动态网络的有限时间同步

复杂网络无处不在,同步是自然界中广泛存在的一类非常重要的非线性现象.过去10年,人们对复杂网络的同步开展了系统而深入的研究,包括恒等同步、广义同步、簇同步以及部分同步等.上述大部分结果中对同步速度的刻画往往是渐进的,只有当时间趋于无穷的时候,网络才能实现同步,而对于网络能够在多长时间内可以实现同步却知之甚少.作者以几类典型的非线性耦合的复杂动态网络为例,深入探讨了复杂动态网络的有限时间同步的规律.具体而言,基于上述几类典型的复杂动态网络,证明了在某些合适的条件下,网络能够在有限时间内实现精确同步.此外,用一个典型的数值仿真实例验证了上述有限时间同步的准则.有限时间同步有效地避免了网络只有在无穷时刻才能实现同步的问题,对网络同步的实际工程应用具有基本的现实意义.     

具有变时滞耦合部分非恒定节点复杂网络的同步(英文)

主要研究了带有时变耦合部分且非恒定节点含有变时滞复杂网络的同步问题.利用Lyapunov函数理论,设计有效的控制函数并获得一些简单的同步准则,使得属于不同簇的复杂网络能同步到任意光滑的状态.最后给以一数值仿真的例子验证了该理论的有效性.     

具有时滞和非时滞耦合的复杂动态网络的自适应同步

对于同时具有时滞耦合和非时滞耦合的复杂动态网络,以时滞动力系统的稳定性理论为基础,设计了全新的自适应控制器,同时给出了一些简单而又一般的网络同步化准则.对由三个节点组成的动态网络的同步化进行了数值模拟,使得理论分析与数值模拟得到了相互验证.     

Group synchronization in complex dynamical networks with different types of oscillators and adaptive coupling schemes

This paper focus on schemes and corresponding criteria for group synchronization in complex dynamical networks consisted of different group of chaotic oscillators. The global asymptotically stable criteria for a linearly or adaptively coupled network are derived to ensure each group of oscillators synchronize to the same behavior. Theoretical analysis and numerical simulation results show that the group synchronization can be guaranteed by enhancing the external coupling strength whenever there are connections or not within the groups under the “same input” condition. All of the results are proved rigorously. Finally, a network with three groups, a scale-free sub-network, a small-world sub-network and a ring sub-network, is illustrated, and the corresponding numerical simulations verify the theoretical analysis.     

Finite-time uniform stability of functional differential equations with applications in network synchronization control

In this paper, we investigate finite-time uniform stability of functional differential equations with applications in network synchronization control. First, a Razumikhin-type theorem is derived to ensure finite-time uniform stability of functional differential equations. Based on the theoretical results, finite-time uniform synchronization is proposed for a class of delayed neural networks and delayed complex dynamical networks by designing nontrivial and simple control strategies and some novel criteria are established. Especially, a feasible region of the control parameters for each neuron is derived for the realization of finite-time uniform synchronization of the addressed neural networks, which provide a great convenience for the application of the theoretical results. Finally, two numerical examples with numerical simulations are provided to show the effectiveness and feasibility of the theoretical results.