The resonance behavior in two coupled harmonic oscillators with fluctuating mass

Abstract

This paper studies the resonance behavior in two coupled harmonic oscillators with fluctuating mass. Firstly, the statistic synchronization between the two particles is obtained and defined. Then, the analytical expression of the output amplitude gain is derived by using the stochastic averaging method. Based on the analytical result and some corresponding numerical results, we analyze the coupling’s influence on the resonance behaviors of the output amplitude gain, including the parameter-induced stochastic resonance, the bona fide resonance, and the stochastic resonance. In weak coupling region, the coupling can not only enhance or weaken the resonance behaviors, but also change the resonance forms. In strong coupling region, the two particles are forced together by the coupling force and move synchronously; thus, the coupling’s influence will vanish. Finally, some numerical simulations are performed to provide a verification and an intuitive understanding of the theoretical results.