关于耦合网络间同步控制的一个注记

本文旨在研究具有相互作用的两个网络间的同步及其控制问题,从理论上我们证明了通过选择适当的控制项,两个网络可以达到同步．文中没有限制两个网络具有相同的动力学,针对两个网络的拓扑结构和网络问的作用矩阵,我们提出了两种自适应同步格式,最后通过数值算例来阐述我们得到的理论结果．     

两个非线性耦合网络间的自适应同步

本文研究了带非线性信号连接的两个复杂网络间的同步问题,引入非线性耦合参数α来调节两个复杂网络的同步．若耦合参数不能保证网络达到外部同步,这里我们提出了一种自适应同步方式,通过此方式可以使两个复杂网络达到同步,最后通过简单的数值算例来阐述得到的理论结果,包括网络具有相同和不相同的拓扑结构两种情形．     

基于终端滑模控制的扰动复杂网络的有限时间同步

本文研究了扰动的复杂网络的有限时间同步问题. 利用终端滑模控制的方法, 设计了能保证网络同步的滑模面和控制器, 得到了两个不同的复杂网络之间达到有限时间同步的充分条件. 这些理论结果推广了复杂网络同步的一些已有结论.     

基于终端滑模控制的扰动复杂网络的有限时间同步（英文）

本文研究了扰动的复杂网络的有限时间同步问题.利用终端滑模控制的方法,设计了能保证网络同步的滑模面和控制器,得到了两个不同的复杂网络之间达到有限时间同步的充分条件.这些理论结果推广了复杂网络同步的一些已有结论.     

基于同步的有向相互依存网络骨干结构识别

本文探讨了由两个子网构成的有向相互依存网络的骨干结构识别问题.基于李雅普诺夫稳定性理论、自适应同步控制技术和线性矩阵不等式(LMI)方法,本文提出了使得驱动网络和响应网络达到自适应同步的充分条件.这些条件使得在网络达到同步的同时,获得驱动网络的骨干结构的识别.最后的数值模拟验证了本文所提出的理论的正确性和有效性.     

具有延时的分数阶神经网络的非脆弱Mittag-Leffler同步

讨论了具有延时的间断分数阶神经网络的全局非脆弱Mittag-Leffier同步,在设计的具有两种波动类型的非脆弱控制器的作用下,利用Lyapunov函数法,非光滑理论,矩阵不等式技巧等,建立了具有线性矩阵不等式形式的系统同步的充分性判据.最后,通过一个数值算例验证了设计控制器的可行性及所得理论的正确性和有效性.     

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.     

一类节点数不同的不确定时空网络的指数外同步

研究了节点数不同的不确定时空网络的指数外同步问题.首先,基于Lyapunov稳定性定理,通过设计合理的控制器,实现了两个节点数不同的不确定时空网络的指数外同步.进一步确定了表示网络拓扑结构的耦合矩阵元和反馈强度的自适应律.最后,以一维Burgers系统和Logistic系统构成的时空网络为例进行了仿真模拟.结果表明,整个网络存在稳定的指数外同步现象.并且同步的速率依赖于可调参数,而网络节点数不影响整个网络同步的稳定性,说明该同步方案具有一定的普适性.     

耦合网络间的有限时聚类改进投影同步

给出自适应控制下,两个不同拓扑的耦合网络在有限时实现聚类改进投影同步的充分条件.首先,根据聚类改进投影同步的定义以及对角矩阵排列因子(scaling factor),得出误差系统的具体形式.然后通过设计恰当的自适应控制器和李雅普诺夫函数,在已有的引理支撑下,得出两个不同拓扑的耦合网络之间的同步准则.结论 表明该有限时聚...     

两个网络间的相互同步

本文研究了两个耦合网络的相互同步,利用线性化方法,我们给出了两个具有相同拓扑结构的网络实现同步的定理,最后用数值例子来验证得到的理论结果。     

Cluster synchronization in colored community network with different order node dynamics

In this paper, a colored community network model with different order nodes dynamics is introduced for the first time. The color of nodes or edges are assumed to be identical if they belong to the same community and nonidentical if they belong to different communities. The color of edges between any pair of communities are assumed to be identical if they connect the same pair of communities and nonidentical if they connect different pair of communities. Further, the order of the node dynamics in different communities can be totally different. Firstly, based on the Lyapunov stability theory, adaptive feedback controllers are designed for achieving cluster synchronization. Secondly, periodically intermittent controllers are designed for achieving cluster synchronization and the synchronization conditions are derived by using mathematical induction method and the analysis technique. Finally, several numerical examples are provided to illustrate the effectiveness of the derived theoretical results.     

Impulsive synchronization of a general nonlinear coupled complex network

This paper investigates impulsive synchronization of a general nonlinear coupled complex network. Based on the comparison theory of impulsive differential system, some novel synchronization criteria are derived, and impulsive controllers are designed simultaneously. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.     

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.     

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.     

Hybrid projective synchronization of complex Duffing–Holmes oscillators with application to image encryption

Many works on hybrid projective synchronization (or simply ‘HPS’ for short) of nonlinear real dynamic systems have been performed, while the HPS of chaotic complex systems and its application have not been extensively studied. In this paper, the HPS of complex Duffing–Holmes oscillators with known and unknown parameters is separately investigated via nonlinear control. The adaptive control methods and explicit expressions are derived for controllers and parameters estimation law, which are respectively used to achieve HPS. These expressions on controllers are tested numerically, which are in excellent agreement with theory analysis. The proposed synchronization scheme is applied to image encryption with exclusive or (or simply ‘XOR’ for short). The related security analysis shows the high security of the encryption scheme. Concerning the complex Duffing–Holmes oscillator, we also discuss its chaotic properties via the maximum Lyapunov exponent. Copyright © 2017 John Wiley & Sons, Ltd.     

Universal chaos synchronization control laws for general quadratic discrete systems

This paper addresses the reliable universal synchronization problem between two coupled chaotic quadratic discrete systems. A general nonlinear control method of synchronization for coupled 2D and 3D quadratic dynamical systems in discrete-time is proposed. The proposed synchronization method is based on universal controllers. The synchronization results are derived theoretically using active control method and Lyapunov stability theory. Numerical simulations are performed to assess the performance of the presented analysis.     

Adaptive synchronization to a general non-autonomous chaotic system and its applications

In this paper, new adaptive synchronous criteria for a general class of n-dimensional non-autonomous chaotic systems with linear and nonlinear feedback controllers are derived. By suitable separation between linear and nonlinear terms of the chaotic system, the phenomenon of stable chaotic synchronization can be achieved using an appropriate adaptive controller of feedback signals. This method can also be generalized to a form for chaotic synchronization or hyper-chaotic synchronization. Based on stability theory on non-autonomous chaotic systems, some simple yet less conservative criteria for global asymptotic synchronization of the autonomous and non-autonomous chaotic systems are derived analytically. Furthermore, the results are applied to some typical chaotic systems such as the Duffing oscillators and the unified chaotic systems, and the numerical simulations are given to verify and also visualize the theoretical results.     

Lag synchronization of complex networks via pinning control

This paper mainly investigates the lag synchronization of complex networks via pinning control. Without assuming the symmetry and irreducibility of the coupling matrix, sufficient conditions of lag synchronization are obtained by adding controllers to a part of nodes. Particularly, the following two questions are solved: (1) How many controllers are needed to pin a coupled complex network to a homogeneous solution? (2) How should we distribute these controllers? Finally, a simple example is provided to demonstrate the effectiveness of the theory.