Van der Pol-Duffing耦合系统的分岔与混沌控制  

Chaos Controlling and Bifurcation of Van der Pol-Duffing System

作　　者：褚衍东[1] 李险峰[1] 张建刚[2] 

机构地区：[1]兰州交通大学数理软件与工程学院,甘肃兰州730070 [2]兰州交通大学非线性研究中心,甘肃兰州730070

出　　处：《江南大学学报（自然科学版）》2007年第1期119-123,共5页Joural of Jiangnan University (Natural Science Edition)　

基　　金：甘肃省自然科学基金项目(3ZS042-B25-049)

摘　　要：用平均法和Melnikov-Holmes方法选取了Van der Pol-Duffing非线性耦合系统的一组能发生混沌的参数.通过Poincaré截面图、分岔图、功率谱图和最大Lyapunov指数图,分析了系统在周期激振力作用下的非线性行为和运动复杂性.最后对系统的混沌运动状态进行了有效的控制.The research selected a set of parameters which could conduce chaos of Van der Pol - Duffing system by averaging method and Melnikov-Holmes method. The paper investigated the influence on the global dynamics behaviors by the change of forced excitation. The very rich and multiplex nonlinear dynamics of the Van der Pol-Duffing oscillator was investigated by theoretical and numerical simulation with the tiny change of the system parameters. The characteristics of chaos attractors of the system were analyzed by the Poincaré map. By simulating the bifurcation diagrams, we demonstrated exactly periodic and chaos motions under the presented parameters. By computing time series Lyapunov exponents and Lyapunov dimensions of Van der Pol-Duffing oscillator, we analyzed the chaos characteristics of the system. Finally, two effective controlling methods were applied to controlling chaos of the system.

关 键 词：分岔 混沌 混沌控制 最大LYAPUNOV指数 POINCARÉ截面 

分 类 号：O322[理学—一般力学与力学基础]