细长刚体块系统中的混沌现象及其Lyapunov指数谱计算

Calculation of Lyapunov exponential spectrum of chaotic phenomena in a slender rigid block system

本文根据细长刚体块系统的特征推广了一类结合局部映射和Poincaré映射计算系统Lyapunov指数谱的方法.通过数值模拟,本文找到了该系统在外部周期激励下通过异宿分岔产生的混沌轨道,并利用推广的Lyapunov指数谱计算方法进行了验证.

In this paper, based on the characteristics of a slender rigid rocking block system, a method is introduced for computing the spectrum of the Lyapunov exponent by combining the local map and the Poincaré map. Then, by numerical simulation, the chaotic orbits under certain parameter conditions generated by heteroclinic bifurcation under external periodic excitation are observed and the extended Lyapunov exponential spectrum method is applied to the rocking block system. Numerical results confirm that the chaotic phenomenon does occur in the system.