CHAOTIC MOTION IN PERTURBATIONS OF SIMPLE PENDULUM AND HARMONIC OSCILLATOR UNDER BOUNDED NOISE EXCITATION
有界噪声激励下单摆-谐振子系统的混沌运动

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.