超混沌时滞神经网络的同步及其仿真  

Synchronization and Simulation of Hyperchaotic Neural Networks with Time-delay

作　　者：张栋[1] 徐鉴[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《系统仿真学报》2010年第3期626-629,633,共5页Journal of System Simulation

基　　金：国家自然科学基金重点项目(10532050);国家杰出青年基金项目(10625211);上海市优秀学科带头人计划项目(08XD14044)

摘　　要：时滞神经网络是解空间为无穷维的非线性动力系统,这样的系统可产生具有多个正的Lyapunov指数的超混沌行为。复杂的时间序列使得这类系统特别适用于保密通信中。针对一类时滞超混沌神经网络系统,利用单向耦合同步概念,设计了一个非线性控制器,并通过Lyapunov-Krasovskii方法和Halanay不等式引理分别给出了系统渐进同步和指数同步的与时滞无关的充分条件。通过引入控制矩阵正定的条件,避免了繁复的LMI计算,简化了控制过程。数值仿真验证了该方法的有效性,数值计算给出了指数同步率和控制参数的关系。The neural networks with time-delay are infinite-dimension nonlinear dynamic systems. They could exhibit hyperchaotic behaviors with multiple positive Lyapunov exponents. This class of systems can be well used in the field of secure communications because of their complex time-series. It deals with the asymptotic and exponential synchronization problems of a class of hyperchaotic neural networks with time-delay. Using the single-direction coupling concept, a nonlinear controller was designed to achieve the state synchronization of two identical hyperchaotic neural networks. Furthermore, based on the L-K method and Halanay inequality lemma, time-delay independent sufficient conditions on synchronization were derived. The complicated calculation of LMI was avoided and the controlling processes were simplified as the consideration of that controller gain matrixes were positive definite. The illustrative examples demonstrate the effectiveness of the synchronization scheme presented. The relationship of exponential synchronization rate and controlling parameters were given by the numerical calculation in the end.

关 键 词：超混沌同步 时滞神经网络 L-K方法 Halanay不等式引理 保密通信 

分 类 号：TN918.1[电子电信—通信与信息系统]