Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation

Abstract

With both analytical and numerical methods, chaotic motions of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation are investigated in this paper. Chaos arising from homoclinic or heteroclinic intersections is studied with the Melnikov method. Chaos threshold is obtained and chaotic feature on the system parameters is investigated in detail. Some new interesting dynamic phenomena including “controllable frequency interval”, “chaotic band” and “uncontrollable parameters” are presented and proved rigorously. Numerical simulations are given to verify chaos threshold obtained by the analytical results.