复杂动力网络的鲁棒性同步

本文研究了扰动下复杂动力网络的同步问题. 利用输入状态稳定性分析的方法, 给出了鲁棒同步的概念, 分析了非时间延迟的和含有时间延迟动力网络的同步, 数值仿真也验证了结果的有效性.     

Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

This paper investigates the problem of function projective synchronization for general complex dynamical networks with time delay. A hybrid feedback control method is designed to achieve function projective synchronization for complex dynamical networks, one with constant time delay and one with time-varying coupling delay. Numerical examples are provided to show the effectiveness of the proposed method.     

Synchronization of singular complex dynamical networks with time-varying delays

This paper considers delay dependent synchronizations of singular complex dynamical networks with time-varying delays. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition for synchronization in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.     

Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

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.     

Projective lag synchronization of the general complex dynamical networks with distinct nodes

In this paper, projective lag synchronization of the general complex dynamical networks with different nodes is investigated. Combining Barbalat’s lemma with adaptive control technique, the adaptive feedback controllers are constructed to achieve projective lag synchronization between the dynamical network with diverse nodes and arbitrary desired trajectory. The presented synchronization method can be applied to any complex networks. It is discovered that the update gains, the time delay, the network size and the network topology have influence on the synchronization effect. Furthermore, projective lag synchronization of the dynamical networks can still be efficiently realized in presence of noise and parameter perturbations. Corresponding numerical simulations are performed to validate the effectiveness and robustness of the proposed synchronization scheme.     

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes is investigated in this paper. Based on Barbalat’s lemma, some sufficient synchronization criteria are derived by applying the nonlinear feedback control. Although previous work studied function projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In our work, the dynamics of the nodes of the complex networks are any chaotic systems without the limitation of the partial linearity. In addition, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. Numerical simulations further verify the effectiveness and feasibility of the proposed synchronization method. Numeric evidence shows that the synchronization rate is sensitively influenced by the feedback strength, the time delay, the network size and the network topological structure.     

Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays

In this article, we consider a generalized complex dynamical network model with nonsymmetric coupling, and the dynamics of each node has a different time-varying delay. Criteria of exponential synchronization are derived in terms of linear matrix inequalities for the model by constructing suitable Lyapunov functionals. The obtained outcomes are different from those in the current literature, in which the complex dynamical networks are coupling symmetrically and delays are fixed constants. Moreover, the given sufficient conditions extend current available results and are verifiable. A numerical example is provided to illustrate the efficiency of the derived outcome.     

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.     

Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems

This paper studies the synchronization problem of complex dynamical networks with stochastic delay which switches stochastically among several forms of time-varying delays. Both the discrete and distributed delays are considered, as well as the Markovian jump parameters. The occurrence probability distribution of the stochastic delay is assumed to be known in prior. By utilizing the Lyapunov–Krasovskii stability theory and stochastic analysis techniques, some sufficient exponential synchronization criteria are obtained, which depend not only on the size of delays, but also on the occurrence probability distribution of the stochastic delay. Moreover, the main results are successfully extended to multi-agent systems with stochastic delay. Several numerical examples are given to illustrate the feasibility and effectiveness of the proposed methods.     

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.     

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.     

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.     

Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation

In this paper, the generalized outer synchronization between two different delay-coupled complex dynamical networks with noise perturbation is investigated. With a nonlinear control scheme, the sufficient condition for almost sure generalized outer synchronization is developed based on the LaSalle-type invariance principle for stochastic differential equations. Numerical examples are examined to illustrate the effectiveness of the analytical results. The theoretic result is also applied to investigate the outer synchronization between two delay-coupled Hindmarsh–Rose neuronal networks with noise perturbation.     

Synchronization for a class of complex dynamical networks with time-delay

In this study, the synchronization problem is addressed for a class of complex dynamical networks in which every identical node is a time-delayed Lur’e system. Delay-dependent and delay-independent synchronization criteria are established through a decoupling technique, which reduces a group of high-dimensional linear matrix inequalities (LMIs) to the test of two groups of lower-dimensional LMIs. An extension to the synchronization of discrete-time Lur’e networks with time delay is also studied. The efficiency and applicability of the proposed methodology is demonstrated by a numerical example through simulation.     

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.     

Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling

In this paper, a general model of an array of N linearly coupled delayed neural networks with Markovian jumping hybrid coupling is introduced. The hybrid coupling consists of constant coupling, discrete and distributed time-varying delay coupling. The complex dynamical network jumps from one mode to another according to a Markovian chain, where all the coupling configurations are also dependent on mode switching. Meanwhile, all the coupling terms are subjected to stochastic disturbances which are described in terms of a Brownian motion. By adaptive approach, some sufficient criteria have been derived to ensure the synchronization in an array of jump neural networks with mixed delays and hybrid coupling in mean square. Surprisingly, it is found that complex networks with two different structure can also be synchronized according to known probability matrix. Finally, an example illustrated by switching between small-world networks and nearest-neighbor networks is given to show the effectiveness of the proposed criteria.     

Non‐fragile synchronization control for complex networks with additive time‐varying delays

In this article, a synchronization problem for complex dynamical networks with additive time‐varying coupling delays via non‐fragile control is investigated. A new class of Lyapunov–Krasovskii functional with triple integral terms is constructed and using reciprocally convex approach, some new delay‐dependent synchronization criteria are derived in terms of linear matrix inequalities (LMIs). When applying Jensen's inequality to partition double integral terms in the derivation of LMI conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. To handle such a combination, an effective method is introduced by extending the lower bound lemma. Then, a sufficient condition for designing the non‐fragile synchronization controller is introduced. Finally, a numerical example is given to show the advantages of the proposed techniques. © 2014 Wiley Periodicals, Inc. Complexity 21: 296–321, 2015     

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.     

Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays

The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.