摘要
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.
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 nonline- arities 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 behav- iors and chaotic motions in the nonlinear nano-oscillator.
基金
supported by the National Natural Science Foundation of China(Grant Nos.11290152,11072008 and 11372015)
the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHRIHLB)
