有界噪声激励下单摆-谐振子系统的混沌运动

CHAOTIC MOTION IN PERTURBATIONS OF SIMPLE PENDULUM AND HARMONIC OSCILLATOR UNDER BOUNDED NOISE EXCITATION

研究了具有同宿轨道和周期轨道的可积单摆-谐振子系统在弱Hamilton摄动(即弱耦合摄动)和弱非Hamilton摄动(即阻尼和有界噪声微扰)下的混沌运动.用Melnikov方程预测Hamilton系统中可能存在混沌运动的参数域,并用Poincare截面验证解析结果.用数值方法计算了有阻尼与有界噪声激励下系统的最大Lyapunov指数和Poincare截面,结果表明有界噪声在频率上的扩散减小了引发系统产生混沌运动的效应.

This paper investigates the chaotic motion in Hamiltonian (i.e. small coupling perturbation) and non-Hamiltonian perturbations(i.e. damping and bounded noise perturbation) of integrable simple pendulum and harmonic oscillator system which contains homoclinic and periodic orbits. The Melnikov's method is used to predict the parameter range for the probably existence of chaotic dynamics in the Hamiltonian system. Poincare maps of the Hamiltonian perturbed system are studied to test the analytical result. The largest Lyapunov exponents and Poincare maps of damped and bounded noise excited system are calculated numerically. It is found that the diffusion of frequency reduces the effect of bounded noise on triggering chaos in the system.