一个新混沌系统的非线性反馈同步控制  

Nonlinear Feedback Synchronization Control of a New Chaotic System

作　　者：张莉[1] 俞建宁[2] 安新磊[2] 彭建奎[3] 

机构地区：[1]兰州工业高等专科学校基础学科部,兰州730050 [2]兰州交通大学数理与软件工程学院,兰州730070 [3]甘肃联合大学,兰州730000

出　　处：《武汉理工大学学报（交通科学与工程版）》2009年第4期811-814,共4页Journal of Wuhan University of Technology（Transportation Science & Engineering）

基　　金：甘肃省自然科学基金项目资助(批准号:3ZS051-A25-030;3ZS-042-B25-049)

摘　　要：提出三维连续自治混沌系统,该系统含有4个参数,3个非线性乘积项,并且每个方程均具有不同的非线性乘积项.利用理论推导、数值仿真、分岔图等对系统的基本动力学特性进行了分析.研究表明,该系统存在着复杂的混沌吸引子,系统具有5个平衡点,与以往研究的Lorenz,Chen等混沌系统是非拓扑等价的;在不同的参数范围下系统可以由混沌态转为稳定的周期轨道,系统由倍周期序列通向混沌.基于Lyapunov稳定性理论,采用非线性反馈控制方法,给出系统在不同初值下实现自同步的充分必要条件及控制律参数的选取范围,数值仿真证明了该方法的有效性.The three-dimensional continuous autonomous chaotic system is studied. The new system contains four system parameters and three quadratic cross-product terms. Each equation contains a single different quadratic cross-product term. Basic dynamic properties of the new system are studied via theoretical analysis and numerical simulation and bifurcation diagram. The studies show that this system has complex attractor and five equilibria, so this system is not topologically equivalent to the Lorenz and Chen systems. When system parameters satisfy different conditions the new system is chaotic or periodic orbit . The system has a progress of flip bifurcation. Based on Lyapunov stabilization theory and nonlinear feedback control method, the sufficient conditions and range of the controller＇s parameter for self-synchronization of chaotic systems are derived. Simulation results proved the proposed synchronization method.

关 键 词：混沌同步 反馈控制 分岔 混沌系统 相图 

分 类 号：O232[理学—运筹学与控制论]