参外联合激励复合非线性振子的分岔分析

讨论了参外联合激励复合非线性振子的动力学行为.对其定常解在一阶近似下的方程进行了局部分岔分析，给出了简单分岔和Hopf分岔发生的条件，并通过对近似方程和原系统的数值模拟加以验证.分析了多种参数对该振子动力学行为演化过程的影响.根据全局分岔理论探讨了该振子在不同条件下发生同宿、异宿分岔的必要条件，其结论与数值计算的结果大致符合. 关键词： 复合非线性振子 局部分岔 全局分岔 混沌

Bifurcation analysis of a compound oscillator with parametric and external excitation

The dynamics of a compound oscillator with parametric and external excitation has been investigated. Local bifurcation analysis of the first order approximation shows that simple bifurcation as well as Hopf bifurcation may take place，as have been observed in the original system. The influence of several parameters on the dynamics has been explored，which reveals that different nonlinear behaviors can be obtained with the variation of the parameters. Furthermore，by employing global bifurcation theory，the necessary conditions for homoclinic and heteroclinic bifurcation has been presented，which agrees well with the numerical results.