Homoclinic chaos in averaged oscillator subjected to combined deterministic and narrow-band random excitations

In the present paper, homoclinic chaos in averaged oscillator subjected to combined deterministic and narrow-band random excitations is investigated in detail. The method of multiple-scale is first used to reduce the oscillator subjected to combined deterministic and narrow-band random excitations to an averaged oscillator only under narrow-band random excitation. In order to determine the threshold of random excitation amplitude for the onset of chaos, the stochastic Melnikov technique is then applied to the averaged oscillator with mean-square criterion and it is found that the threshold of random excitation amplitude for the onset of chaos in the oscillator turns from increasing to decreasing as the intensity of the noise increases. On the other hand, another threshold of random excitation amplitude for the onset of chaos is obtained by calculating the largest Lyapunov exponents numerically. The Poincare maps are also used for verifying the conclusion. Qualitatively consistent results are obtained by the analytical and numerical methods.