Stochastic Resonance in Coupled Underdamped Harmonic Oscillators with Fluctuating Frequency Driven by Dichotomous Noise

Abstract

In this paper, the resonance behaviors of two coupled harmonic oscillators with fluctuating frequency driven by an external periodic signal are investigated. Applying the Shapiro–Loginov formulas and the Laplace transform technique, the statistic synchronization between the two particles is observed and defined. Based on this finding, the analytical expression of the output amplitude gain (OAG) is derived. It is shown that the OAG is a non-monotonic function of the system parameters. The influences of the coupling strength as well as the other parameters on the resonance behaviors of OAG are discussed, including parameter-induced stochastic resonance, bona fide resonance and stochastic resonance. It is found that weak coupling can not only affect the resonance strength, but also change the resonance form. On the other hand, strong enough coupling can bind the particles together to move as a whole. In this case, the influence of the coupling will vanish. Furthermore, some numerical simulations are presented to verify the effectiveness of the theoretical analysis results.