非线性动力系统周期解的伪不动点追踪算法及应用

Relationship between Periodic Solutions of Nonlinear Dynamic Systems

文中提出一种求解非线性动力系统稳定及不稳定周期解的新的思路和方法，它由寻找非线性动力系统同时存在的各个周期解间的联系入手，引入一个反映系统全局瞬态信息的标量函数．将非线性动力系统求各个周期解的问题转化为此标量函数的寻优问题，并以非线性轴承转子系统这一典型的倍周期分叉系统为例，顺序求得了Ｔ和２Ｔ周期解，从而揭示了这２个周期解间的内在联系．

Stable and unstable periodic solutions are discussed on nonlinear dynamic systems. Treated as a local or global optimization problem, relation among periodic solutions is established. As an example, two solutions with period T and 2 T are used to yield their relation of the nonlinear bearing rotor system.