倒置单摆在拟周期扰动下的同宿分岔

Homoclinic bifurcation in quasiperiodically forced inverted pendulum

为讨论一类具有双侧刚性约束的非线性倒置单摆的同宿轨在含有两个基本频率的拟周期外力扰动下的分岔,本文将原本适用于光滑系统的Melnikov方法推广到了此类系统并导出了相应的Melnikov函数的计算公式,由此给出了扰动系统稳定流形与不稳定流形横截相交的一个充分条件.

We discuss the homoclinic bifurcation for a nonlinear inverted pendulum impacting between two rigid walls under external quasiperiodic excitation with two fundamental frequencies.The Melnikov method established for smooth dynamical systems is extended to be applicable to the general quasiperiod-ic excited impact system.We present a method to compute the first order Melnikov function to derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally.