Melnikov chaos in Duffing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations

In this paper, the dynamic behavior of Duffing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations is investigated. Theoretically, the random Melnikov's method is used to establish the conditions of existence of chaotic motion. The result implies that the chaotic motion of the system turns into the periodic motion with the increase of nonlinear damping parameter, and the threshold of random excitation amplitude for the system to change from chaotic to periodic motion in the oscillator turns from increasing to constant as the intensity of the noise increases. Numerically, the largest Lyapunov exponents and the Poincare maps are also used for verifying the conclusion.