基于LMI的参数未知时变时滞混沌系统模糊自适应H_∞同步

考虑一类结构相同但驱动系统参数未知的两个时变时滞混沌系统同步问题,提出了基于T-S模糊模型的模糊自适应H∞同步方法.基于Lyapunov稳定性理论和线性矩阵不等式技术,给出了驱动系统参数未知时变时滞混沌系统同步的充分条件.仿真结果表明了所提方法的有效性.     

混沌同步的充分条件及应用

对两大类常用连续混沌系统，给出了同步的充分条件，以及状态变量的演化范围，对其作了证明，从理论上分析了这些充分条件一定可实现. 作为应用，证明了时变参数混沌同步的实现充分条件，并用Chua系统仿真实现. 时变参数混沌同步通信具有强抗破译性，也给出其抗破译的仿真. 关键词： 条件Lyapunov指数(CLE) Chua电路 参数同步     

双向耦合混沌系统的反同步性研究

针对两个双线性耦合的统一混沌系统，通过运用自适应方法实现它们的完全反同步.自适应控制器和耦合系数均由Lyapunov稳定性理论和最小值定理估计出来，这种方法并不需具体求出耦合系数范围，也无需事先知道耦合混沌系统的最大值，就能实现反同步.将这种方法应用到Chen-Chen混沌系统的双向耦合情况，数值仿真表明该方法的有效性和实用性. 关键词： 统一混沌系统 双线性耦合 自适应反同步     

基于线性耦合下混沌系统的同步条件

将混沌同步问题用精确的数学语言给予描述，通过数学分析将其转化为微分方程组的稳定性问题.以Lorenz系统族的Chen氏系统作为典型系统，在线性耦合下分析系统参数，得到了系统达到同步时的充分条件，且在理论上加以证明.结合该条件，提出了一种确定耦合系数的方法.最后用仿真实验验证了该方法的正确性，并验证了在不同耦合方式和参考系统的情况下定理的有效性. 关键词： 混沌同步 耦合 稳定性     

一种新的分段混沌系统的同步控制

利用状态观测器思想构造驱动和响应系统，实现了一个新近提出的分段线性混沌系统的同步控制，并且推导了两个不同初值的系统实现同步的充分条件.理论分析说明该方法对原系统结构没有特殊要求，无需求解Lyapunov函数，适合应用于分段混沌系统.仿真实验的良好结果验证了该算法的有效性，对于不同初值的分段系统均能实现快速同步.同时该算法适用于一类分段混沌系统的同步控制. 关键词： 分段线性混沌系统 状态观测器 同步控制     

基于观测器的混沌广义同步解析设计

提出用改进的状态观测器研究混沌广义同步问题.采用解析法求得了混沌广义同步的响应系统.从状态观测器理论，得到驱动和响应系统全局渐进线性广义同步的充分条件.以超混沌R?ssler系统为例，数值研究了该同步方法.结果表明了它的有效性. 关键词： 混沌 广义同步 状态观测器 R?ssler系统     

自治混沌系统的线性和非线性广义同步

研究了自治混沌系统的广义同步问题.基于改进的状态观测器方法和极点配置技术，提出了一种新的广义同步方案，扩展了混沌广义同步的适用范围，并用该方法实现了自治混沌系统的线性及非线性广义同步.根据状态观测器理论，给出了驱动-响应系统获得全局渐进广义同步的充分条件.数值仿真实验进一步验证了所提方法的有效性. 关键词： 自治混沌系统 广义同步 状态观测器 分段线性Chen系统     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论，得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性. 关键词： 分时切换混沌同步 线性反馈 关联混沌系统     

对称非线性耦合混沌系统的同步

研究两个对称非线性耦合混沌系统的同步问题.通过对系统线性项与非线性项的适当分离， 构造一个特殊的非线性耦合项，发现在耦合强度α＝05附近的某一区域里存在稳定的 混沌同步现象.提供判断同步误差稳定性的方程，利用线性系统的稳定性分析准则和条件Lya punov指数来检验同步状态的稳定性.新方法适用于连续时间系统的混沌同步，也适用于具有 两个（或多于两个）正Lyapunov指数的超混沌系统.以Lorenz系统，超混沌Rssler 系统作 为算例，数值模拟结果证实所提新方法的有效性. 关键词： 混沌 同步 非线性耦合 稳定性准则 超混沌     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论，得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性.     

Adaptive projective synchronization with different scaling factors in networks

We study projective synchronization with different scaling factors （PSDF） in N coupled chaotic systems networks. By using the adaptive linear control, some sufficient criteria for the PSDF in symmetrical and asymmetrical coupled networks are separately given based on the Lyapunov function method and the left eigenvalue theory. Numerical simulations for a generalized chaotic unified system are illustrated to verify the theoretical results.     

一种参数摄动的混沌异结构同步方法

研究了参数摄动情形下的混沌异结构同步问题，基于Lyapunov稳定性定理并结合范数理论给出了系统参数摄动下实现混沌异结构同步的一个充分条件，为同步控制器的设计提供了一般方法.只要两混沌系统维数相等，状态变量可测，就可利用所提方法实现系统参数摄动下的异结构同步，并能够保证在同步实现后同步控制量伴随误差变量一同收敛至零.该方法鲁棒性强，适用范围广，通过对混沌系统、超混沌系统的同步仿真，证实了该方法的有效性. 关键词： 混沌 超混沌 同步 Lyapunov函数     

Complete and generalized synchronization in a class of noise perturbed chaotic systems

In the paper, in light of the LaSalle-type invariance principle for stochastic differential equations, chaos synchronization is investigated for a class of chaotic systems dissatisfying a globally Lipschitz condition with noise perturbation. Sufficient criteria for both complete synchronization and generalized synchronization are rigorously established and thus successfully applied to realize chaos synchronization in the coupled unified chaotic systems. Furthermore, concrete examples as well as their numerical simulations are provided to illustrate the possible application of the established criteria.     

Chaos quasisynchronization induced by impulses with parameter mismatches

This paper studies the effect of parameter mismatch on the impulsive synchronization of a class of coupled chaotic systems. A new definition for global quasisynchronization is introduced and used to analyze the synchronous behavior of coupled chaotic systems in the presence of parameter mismatch. Using the linear decomposition and comparison-system methods, a global synchronization error bound together with a sufficient condition is derived. Numerical simulations on the chaotic Chua's circuit are presented to verify the theoretical results.     

Projective synchronization of chaotic systems with bidirectional nonlinear coupling

This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.     

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.     

Realization of generalized synchronization between different chaotic systems via scalar controller

In this paper, a very simple generalized synchronization method between different chaotic systems is presented. Only a scalar controller is used in this method. The method of obtaining the scalar controller from chaotic systems is established. The sufficient and necessary condition of generalized synchronization is obtained from a rigorous theory, and the sufficient and necessary condition of generalized synchronization is irrelative to chaotic system itself. Theoretical analyses and simulation results show that the method established in this paper is effective.     

New results for exponential synchronization of linearly coupled ordinary differential systems

This paper investigates the exponential synchronization of linearly coupled ordinary differential systems. The intrinsic nonlinear dynamics may not satisfy the QUAD condition or weak-QUAD condition. First, it gives a new method to analyze the exponential synchronization of the systems. Second, two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems. Finally, an application to the linearly coupled Hopfield neural networks and several simulations are provided for verifying the effectiveness of the theoretical results.     

Liu混沌系统的非线性反馈同步控制

研究了新型混沌系统——Liu系统的同步控制问题.基于Lyapunov稳定性理论，采用非线性反馈控制方法，给出了Liu系统实现自同步的充分条件以及控制律参数的取值范围；结合参数自适应控制方法，实现了Liu混沌系统与统一混沌系统的异结构系统快速同步.数值仿真证明了该方法的有效性. 关键词： Liu混沌系统 混沌同步 非线性反馈控制 参数自适应控制     

利用标量控制器实现一类混沌系统同步

研究了一类混沌系统的混沌同步，对此类混沌系统，通过设计一个合适标量控制器，可以实现系统的混沌同步.给出了该标量控制器设计的一般方法，并从理论上得到了混沌同步的充分和必要条件，且此充分和必要条件与混沌系统的性质无关. 关键词： 混沌系统 标量控制器 混沌同步