一类特殊的Mathieu方程的分岔及混沌控制

Chaos Controlling and Bifurcation of a Special Mathieu Function

用相图、Lyapunov指数图、时间响应图、庞加莱截面图和全局分岔图分析和研究了系统的混沌状态.利用耦合反馈控制法对一类特殊的Mathieu方程的混沌行为进行了控制.结果表明,通过这种方法可有效将这一类特殊的Mathieu方程的混沌运动控制到稳定的周期状态.

The chaotic behaviors in a special mathieu function was analyzed by phase diagrams, Lyapunov exponent, Lyapunov dimension, Poincare map and global bifurcation graphs. Controlling the chaotic behaviors are based on the analysis. The chaotic behaviors in a special Mathieu function were controlled by means of the coupled feedback controlling method. By selecting proper controlling parameters according to bifurcation graph, the chaotic motions of the system can be successfully converted to the stable periodic orbits under coupled feedback controlling method.