线性混合耦合切换网络的全局指数同步研究

研究具有子系统时变时延和节点间耦合时延的线性混合耦合切换网络的全局指数同步问题。应用切换系统的稳定性理论对具有特殊切换信号和切换拓扑结构的复杂动态网络的同步性问题进行研究,并以线性矩阵不等式形式给出一个时延相关的充分条件,该条件保证了该类网络在应用平均驻留时间方法时能够达到全局指数同步。最后给出一个实例验证了结论的正确性。     

节点非线性耦合的复杂动态网络同步控制研究

文中研究节点状态非线性耦合的复杂动态网络的局部同步和全局同步的问题.不同于现有的这类网络的利用节点状态变量设计控制器进行同步控制的方法,提出了一种设计同步控制器的新方法,该方法只需利用网络节点输出变量构造控制器,使其达到同步,克服了现有方法利用节点状态变量设计控制器存在的不足,使控制器实现起来更加简单.利用 Lyapunov 方法给出这类复杂网络的同步准则,以 Lorenz 混沌映射作为复杂网络的节点进行数值仿真,研究表明,这种方法能够使节点状态非线性耦合的复杂动态网络达到同步,通过系统仿真,证明了文中所提方法的有效性     

随机Lur’e时滞网络的指数同步与脉冲控制

本文研究了一类具有不对称耦合和时变时滞随机Lur’e动态网络的全局指数同步问题. 为了使网络中的所 有Lur’e系统达到同步, 文章提出了一种实用的脉冲控制策略, 利用平均脉冲间隔概念、Perron-Frobenius定理、比较 原理、参数变分法和无参照系统策略, 给出了保证网络实现全局指数同步的充分条件. 基于脉冲信号既能促进网络 群聚行为同时也可能阻碍网络同步这一事实, 本文分别讨论了积极脉冲效应和消极脉冲效应作用下网络实现同步 的判定方法, 同时给出了不同脉冲效应作用下网络的收敛速度. 提供了数值仿真证明主要结果和控制策略的有效 性.     

单向耦合混沌同步及其在保密通信中的应用

采用单向耦合同步法,利用Lyapunov稳定性定理、全局同步法及最大Lyapunov指数法分别对Lorenz系统、变形耦合发电机系统及超混沌Chen系统的自同步进行了研究.为适用于混沌保密通信,使用单路信号实现了驱动系统与响应系统的同步,并给出将超混沌Chen系统的自同步用于混沌掩盖保密通信的具体例子.数值模拟验证了所给方案的有效性.     

时延复杂网络的自适应周期间歇同步控制

研究同时具有耦合时延和节点时延复杂网络的自适应周期间歇同步控制问题.运用 Lyapunov 稳定性理论,自适应控制、牵制控制和间歇控制方法,给出保证该时延复杂网络全局指数同步、且保守性更小的判定准则,并给出相应的自适应和牵制自适应间歇同步控制器设计,该控制策略对节点间的耦合强度和网络的拓扑结构等具有较强的鲁棒性.最后以时延非线性动力系统为节点对复杂网络进行数值仿真,验证了结论的正确性和有效性.     

无标度网络同步过程研究

在以对称耦合振子为节点的无标度网络中,度的不均匀分布性对网络的全局同步具有抑制作用,使得其同步过程研究比一般连续耦合网络完全同步研究方法更为复杂.论文将非线性系统理论以及稳定性理论等应用到无标度网络同步过程研究中,在每一个节点上引入非线性动态方程,对同步误差的变分进行稳定性分析,来判断节点是否能同步,并分析其研究方法与一般连续耦合网络完全同步研究方法的不同.以R(o)ssler振子构成的无标度网络作为对象进行仿真,仿真结果表明,度的不均匀分布性不仅导致无标度网络的同步性能下降,而且使得它的同步过程具有分层过渡的特点.     

不同节点动态的复杂网络外部同步牵制控制

研究节点动态不同的两个复杂网络的外部同步问题。运用牵制控制方法,网络模型选取节点输出线性耦合模型,基于输出控制思想,设计结构简单的牵制控制器,对响应网络中的部分节点施加输出反馈控制,使得两个复杂动态网络达到外部同步,即实现响应网络与驱动网络的渐近同步。根据李雅普诺夫稳定性理论,推出相应的同步准则,得到控制器参数选择条件。仿真时,驱动网络和响应网络分别选取Lorenz系统和Lu系统,对全局耦合网络和最近邻耦合网络两个典型网络拓扑进行仿真,验证了所提方法的有效性。     

不同节点动态的复杂网络外部同步牵制控制

研究节点动态不同的两个复杂网络的外部同步问题。运用牵制控制方法,网络模型选取节点输出线性耦合模型,基于输出控制思想,设计结构简单的牵制控制器,对响应网络中的部分节点施加输出反馈控制,使得两个复杂动态网络达到外部同步,即实现响应网络与驱动网络的渐近同步。根据李雅普诺夫稳定性理论,推出相应的同步准则,得到控制器参数选择条件。仿真时,驱动网络和响应网络分别选取Lorenz系统和Lü系统,对全局耦合网络和最近邻耦合网络两个典型网络拓扑进行仿真,验证了所提方法的有效性。     

非线性耦合的复杂网络自适应同步

提出了一种通过非线性耦合的复杂网络自适应同步方案,方案具有自适应律简单和应用范围广等特点。证明了动力系统满足给定条件下,该同步方案同步,且同步解是局部和全局渐进稳定的。两个计算机仿真实例分别展示了在无标度网络和最近邻耦合网络上的同步误差变化趋势,验证了同步方案的有效性。     

时变复杂动力学网络的同步控制

研究时变复杂动力学网络的同步控制问题.假定网络模型中的同步轨迹及耦合配置矩阵、内部耦合矩阵的各元素均有界,当这些界值可以预估或不确定时,分别应用线性反馈控制和自适应反馈控制策略使该网络实现全局同步.通过构造Lyapunov函数,证明了对于任意初始状态的时变复杂动力学网络模型在相应的控制手段下总可以实现渐近同步.特别是设计的自适应反馈控制策略对网络的拓扑结构、节点间的耦合强度及时滞等因素表现出较强的鲁棒性.数值仿真证实了上述结论的有效性.     

New Results on Global Synchronization of Chua's Circuit

Some new results on global exponential synchronization and global synchronization for Chua's circuit are derived by means of Lyapunov functions and some other mathematic methods, which improve the existing results in the literatures. A strict and complete proof of the result is also given as a complement to the relevant literature where the proof was incomplete. The paper offers some new approaches for studying chaos synchronization for Chua's circuit.     

Chua电路全局同步的新结果

Some new results on global exponential synchronization and global synchronization for Chua0s circuit are derived by means of Lyapunov functions and some other mathematic methods, which improve the existing results in the literatures. A strict and complete proof of the result is also given as a complement to the relevant literature where the proof was incomplete. The paper offers some new approaches for studying chaos synchronization for Chua0s circuit.     

Some synchronization criteria for bidirectionally-coupled chaotic systems

1IntroductionChaos synchronization,as a very important topic in thenonlinear science ,has been developed extensivelyinthelastfew years [1,2] .A wide variety of approaches [1 ~9]have been proposed for the synchronization of chaoticsystems which include linear and nonlinear feedback,adaptive control ,etc . Most of the methods mentionedabove synchronize two coupled identical chaotic systems .Accordingto the condition of coupling signal ,they can beclassified into bidirectional [3 ~5] and unidirec…     

Some synchronization criteria for bidirectionally-coupled chaotic systems

Based on the stability theory of linear time-varying continuous system,this paper investigates the synchronization of two linear bidirectionally-coupled systems.Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback.Since the trajectory of chaotic system is continuous and bounded,one can choose suitable coupled parameters to satisfy the proposed criterion.The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling.The chaotic Chen system and the generalized Lorenz-like system are taken as examples,the simulations verify the effectiveness of the proposed method.     

Passivity‐based state synchronization of homogeneous multiagent systems via static protocol in the presence of input saturation

This paper studies semiglobal and global state synchronization of homogeneous multiagent systems with partial‐state coupling (ie, agents are coupled through part of their states) via a static protocol. We consider 2 classes of agents, ie, G‐passive and G‐passifiable via input feedforward, which are subjected to input saturation. The proposed static protocol is purely decentralized, ie, without an additional channel for the exchange of controller states. For semiglobal synchronization, a static protocol is designed for an a priori given set of network graphs with a directed spanning tree. In other words, the static protocol only needs rough information on the network graph, ie, a lower bound for the real part and an upper bound for the modulus, of the nonzero eigenvalues of the corresponding Laplacian matrix. Whereas for global synchronization, only strongly connected and detailed balanced network graphs are considered. In this case, for G‐passive agents, the static protocol does not need any network information, whereas for G‐passifiable agents via input feedforward, the static protocol only needs an upper bound for the modulus of the eigenvalues of the corresponding Laplacian matrix.     

Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation

In this paper, the master‐slave synchronization for coupled neural networks with Markovian jumping topology and stochastic perturbation is discussed. Based on a graph theory, the ergodic property of the Markovian chain, and the strong law of the large numbers for local martingales, several sufficient conditions are established to ensure the almost sure exponential synchronization or asymptotic synchronization in mean square for coupled neural networks with Markovian jumping topology. By the pinning control method, the chaotic synchronization between the master system and the slave systems with stochastic disturbance is achieved. The effectiveness of the results is finally illustrated by a numerical example.     

复杂网络的同步及保密通信

本文以当前的研究热点复杂网络为背景．用Lyapunov稳定性理论和矩阵变换研究了网络中互相耦合的三个节点的混沌同步，提出了一种全局混沌同步方案，并在同步的基础上研究了节点之间的保密通信，最后利用Matlab软件进行数值仿真．仿真结果表明了该方法的有效性．