带有2个周期激励外力的Duffing-van der Pol方程的混沌及其控制

Chaos and Control of the Duffing-van der Pol Equation with Two External Periodic Excitations

考虑一类具有五次非线性恢复力项和2个周期激励外力的Duffing-van der Pol方程.通过相图、势能图、Poinc偄re映射图、全局分支图和最大Lyapunov指数图,分析了系统在2个周期激励作用下的非线性行为和复杂的运动状态.最后通过2种有效的方法实现了该系统的混沌控制,将系统的混沌态控制到稳定的周期轨道(或拟周期轨道).

Large Duffing-van der Pol equation with fifth nonlinear-restoring force and two external periodic excitations is investigated.By applying phase diagrams,potential diagram,Poincre maps,bifurcation diagrams and maximal Lyapunov exponent diagrams,the nonlinear behavior and the complex state of the system under the two external periodic excitations are analyzed.At last,two methods are applied to control the chaotic behaviors of the system,effectively to a steady periodic orbit（or quasi-periodic orbit）.