Multi-pulse homoclinic orbits and chaotic dynamics of a parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities

Abstract

In this paper, the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied. The damping, parametrical excitation and the nonlinearities are regarded as weak. The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales. The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method. We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos. At last, numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.