具有拓扑切换特性的离散型不确定时空网络的指数同步

研究了具有拓扑切换特性的离散型不确定时空网络的指数同步问题. 基于稳定性理论, 构造了具有指数形式的Lyapunov函数, 并设计了同步控制器的结构方程, 进而获得了时空网络的同步条件. 同时, 我们设计了未知参数的识别律, 有效地识别了网络中的未知参数. 最后, 选取实际的激光相位共轭波空间扩展系统作为网络节点进行仿真模拟, 验证了同步方案的可行性与控制器的有效性. 通过构造具有指数形式的Lyapunov函数, 能够有效地调节网络的同步速率. 并且获得的同步条件中不包含网络的耦合矩阵项, 消除了拓扑切换特性对同步过程的影响, 使得网络同步性能更加稳定.     

离散混沌网络系统中共同噪声诱导同步的条件

噪声普遍存在于各种真实系统和人造系统中,它对系统的同步动力学具有多重影响.本文探索外部噪声对高维离散复杂网络系统同步行为的积极作用.首先构建外部共同噪声驱动下两个参数相同、未耦合的离散混沌网络模型,然后利用Birkhoff遍历定理与矩阵论等相关理论,严格证明了噪声诱导两个离散混沌网络系统取得同步的充分条件,进一步借助于具体的混沌网络模型,利用数值仿真验证了理论分析的有效性.数值模拟的结果表明当网络模型参数满足理论分析的充分条件时,共同噪声可以诱导两个参数相同、未耦合的离散混沌网络在随机意义下取得同步,而且同步效果不依赖于复杂网络拓扑结构的选取.     

Lorenz系统与Rossler系统的异结构同步

研究了不确定参数的Lorenz系统和Rossler系统的异结构同步问题.基于Lyapunov稳定性理论,采用主动同步,自适应同步两种方法实现异结构混沌系统的同步,并且利用数值模拟来阐释理论的有效性.     

具有间歇耦合的复杂动态网络量化同步分析

讨论了基于量化控制信号的间歇耦合复杂动态网络的同步动力学,根据脉冲间隔周期和量化器的特征,并利用稳定性理论和 Razumikhin 定理,分别给出了含时滞和不含时滞下的复杂动态网络同步化准则.网络节点间在一系列分段周期内有耦合,耦合过程中控制作用通过“对数量化器”对同步误差的反馈控制瞬态信号进行量化.所得理论结果进一步应用于由 Chua 混沌系统为动力节点所构成的复杂动态网络,数值模拟表明了所获理论结果的有效性.     

多层星形网络的特征值谱及同步能力分析

多层网络是当今网络科学研究的一个前沿方向。针对多层双向耦合星形网络的特征值谱对网络的同步能力进行了研究。通过严格推导出多层双向耦合星形网络特征值的解析表达式,分析了节点数、层数、层内耦合强度和层间耦合强度与网络同步能力的关系,重点分析了层数对网络同步能力的影响。网络的同步能力除了受层内耦合强度和层间叶子节点之间的耦合强度影响外,当同步域无界时,若层间叶子节点之间的耦合强度较弱,网络的同步能力还依赖于层数。当同步域有界时,网络的同步能力随节点数、层间中心节点之间的耦合强度增大而变弱;若层内耦合强度较弱,网络的同步能力随层数增大而减弱;若层间叶子节点之间的耦合强度较弱,网络的同步能力随层数增大反而增强。     

基于单向耦合法的不确定复杂网络间有限时间同步

针对具有不确定性的复杂网络有限时间同步问题, 提出一种新颖的单向耦合控制方法. 构建含有未知参量及未知拓扑结构的驱动?响应复杂网络模型, 考虑两个网络具有不同的节点数, 同时受到时变耦合时滞的影响, 并且网络内部分别具有不同的节点系统. 基于有限时间稳定性理论和线性矩阵不等式变换, 通过在响应网络中引入单向耦合项, 实现两个网络间的有限时间同步, 同时准确辨识未知参量及未知拓扑结构. 仿真实验验证所提同步方法的有效性, 对比实验结果表明所提方法在减少耦合数量的同时具有更快的同步速率及更小的波动范围.     

输出耦合的复杂网络自适应脉冲同步

应用自适应脉冲控制策略实现输出耦合复杂网络的同步.通过构造Lyapunov泛函,设计合适的自适应脉冲控器,并利用脉冲微分方程理论,建立了网络的同步准则.该准则保证了动态网络渐进同步于任意指定的网络中的单独节点的状态.数值模拟表明所得控制器的有效性.     

两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识

研究两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识的问题.首先,建立具有耦合时滞以及模型参数不确定分数阶复杂网络模型,并给出驱动网络与响应网络的延迟投影同步误差模型;其次,设计有效的控制器以及参数自适应律以实现两个网络之间的延迟投影同步与参数辨识,给出了实现延迟投影同步与参数辨识的充分条件,对该充分条件给出了...     

一种新型的复杂网络的完全同步

为使得网络的节点间无直接耦合关系且网络可控制达到同步,运用生物系统中群体感应的思想构造了一种通过扩散的外部信号与节点之间的感应而使节点连接的新型复杂网络,并在周期边界条件下,研究了该复杂网络节点的同步问题.根据李亚普诺夫稳定性理论证明了通过控制感应强度,可实现网络中各节点运动的完全同步.数值仿真结果表明了该网络可在周期解处达到同步,且随感应强度不同,周期解的复杂程度不同.     

Bragg激光系统之间信号的同步传输

研究了具有相互耦合的三台Bragg激光系统之间信号的同步传输.在这种同步机理中,前一级激光系统的输出信号被提取一部分线性耦合到下一级激光系统中,逐级驱动多级激光系统达到信号的同步传输.基于稳定性定理,通过计算每个激光系统的Lyapunov指数,确定了实现多级激光器完全同步的条件.     

Synchronization of Uncertain Complex Networks with Time‐Varying Node Delay and Multiple Time‐Varying Coupling Delays

This paper investigates the synchronization problem of a class of complex dynamical networks via an adaptive control method. It differs from existing works in considering intrinsic delay and multiple different time‐varying coupling delays, and uncertain couplings. A simple approach is used to linearize the uncertainties with the norm‐bounded condition. Simple but suitable adaptive controllers are designed to drive all nodes of the complex network locally and globally synchronize to a desired state. In addition, several synchronization protocols are deduced in detail by virtue of Lyapunov stability theory and a Cauchy matrix inequality. Finally, a simulation example is presented, in which the dynamics of each node are time‐varying delayed Chua chaotic systems, to demonstrate the effectiveness of the proposed adaptive method.     

Synchronization of Switched Neural Networks with Time‐varying Delays via Sampled‐data Control

This paper investigates sampled‐data synchronization control of switched neural networks with time‐varying delays under average dwell time. Based on the delay system method, the sampled‐data synchronization system is proposed with time‐varying delays and input delays in the unified framework for switched neural networks. By constructing a suitable Lyapunov‐Krasovskii functional and free‐weighting matrix, the relationship between the average dwell time and the maximum sampling interval is revealed to form delay‐dependent exponentially synchronization criteria. The desired mode‐dependent controller under the maximum sampling interval and decay rate is designed. Finally, two numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed techniques.     

Proportional‐delay adaptive control for global synchronization of complex networks with time‐delay and switching outer‐coupling matrices

In this paper, the global synchronization problem for complex dynamical networks with time‐delay and switching outer‐coupling matrices is studied using the method of adaptive control. The mixed time‐delays in the considered system comprise both discrete time‐varying delay and distributed delay. The outer‐coupling matrices in the complex networks are assumed to vary with time and are described by a Markov process with finite state values. Based on the Lyapunov stability theory, the complete‐square method, and the Kronecker product analysis technique, a sufficient condition, which guarantees the global synchronization of all of nodes is obtained. The updated laws of controller do not only depend on the lag states of the complex dynamical networks but also depend on the Markov process. Finally, a numerical example is provided to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

时变耦合复杂网络的有限时间广义外部同步

研究了两个具有时变耦合矩阵的复杂动态网络的有限时间广义外部同步的问题。设计了有限时间控制器, 使两个网络能在有限时间内实现外部同步。利用微分方程的有限时间稳定性理论,得到了复杂网络实现有限时间外部同步的充分条件。为了验证所提方案的有效性,给出了仿真算例,算例验证了有限时间广义外部同步方案的有效性。     

Crossed Synchronization of Multiple Subnets Complex Network System with Time‐Varying Delay

A dual‐time varying delay complex network system is formed by a plurality of sub‐networks. This paper discusses the crossed synchronization stability of such systems on the basis of crossed synchronization definition between the sub‐nets. By the Lyapunov stability theory with the Zero Theorem, we obtained a sufficient condition that a synchronization exponentially stable controller exists in the complex network system, with characteristic variable delay. The relationship between the complex network nodes are discussed, and the two nodes must be connected and can interact with each other so it has the actual coupling strength. Finally, combining the given conditions, a numerical simulation illustrates its effectiveness.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Synchronization of uncertain complex dynamical networks via adaptive control

In this paper, synchronization of an uncertain dynamical network with time‐varying delay is investigated by means of adaptive control schemes. Time delays and uncertainties exist universally in real‐world complex networks. Especially, parameters of nodes in these complex networks are usually partially or completely uncertain. Considering the networks with unknown or partially known nodes, we design adaptive controllers for the corresponding complex dynamical networks, respectively. Several criteria guaranteeing synchronization of such systems are established by employing the Lyapunov stability theorem. Analytical and numerical results show that the proposed controllers have high robustness against parameter variations including network topologies, coupling structures, and strength. Copyright © 2008 John Wiley & Sons, Ltd.     

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.