一类Mathieu方程的混沌分析及控制  

Analysis and Control of Chaos for a Sort of Mathieu Equation

作　　者：高先锋[1] 李险峰[2] 张建刚[2] 

机构地区：[1]鲁东大学网络中心,山东烟台264025 [2]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《湖北民族学院学报（自然科学版）》2007年第4期389-392,共4页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：甘肃省自然科学基金项目(3ZS042-B25-049);鲁东大学科研基金项目(L20062301);兰州交通大学科研基金项目(DXS-07-0028;DXS-07-0029)

摘　　要：利用数值仿真的方法,对一类Mathieu方程的混沌运动及其控制进行了研究.利用分岔图、Lyapunov指数谱和相图等揭示了该系统经由倍周期分岔通向混沌的路径.采用二次分段函数作为非线性反馈控制器,通过控制后方程的分岔图选择适当的控制参数,对这一类Mathieu方程中的混沌行为进行有效的控制.By means of numerical simulations, the bifurcation and the chaotic behaviors of a nonlinear Mathieu function are studied. The route to chaos is revealed by global bifurcation diagram. Phase portraits, bifurcation diagram and Lyapunov - exponent spectrum are also presented to analyze nonlinear dynamics of the system. The method,which is a subsection square function, is adopted as the nonlinear feedback controller to control chaos in this paper. By selecting proper controlling parameters according to bifurcation diagrams, the chaotic motions of the system can be successfully converted to different stable periodic orbits. The results are demonstrated and illustrated by reverse periodic - doubling bifurcation diagrams and phase portraits.

关 键 词：分岔 混沌 混沌控制 POINCARÉ映射 

分 类 号：O322[理学—一般力学与力学基础]