Trichotomous noise induced resonance behavior of two coupled harmonic oscillators with fluctuating mass

This paper investigates the stochastic resonance phenomenon in two coupled harmonic oscillators with fluctuating mass. The fluctuation of the mass is modeled as a trichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform, the statistic synchronization between the two particles is obtained and defined. Then, the analytical expression of the output amplitude gain is derived. Based on the analytical result, the influence of the trichotomous noise'steady-state probability and the coupling strength on the resonance behaviors of the output amplitude gain are discussed. In the strong noise region, the output amplitude gain of the system will exhibit stochastic resonance with change of the steady state probability, so that the system output amplitude gain induced by trichotomous noise is greater than induced by dichotomous noise. Beside, the system output amplitude gain has resonance behavior with respect to the coupling strength too. Unlike the case of dichotomous noise, the system's output amplitude gain can show double-peaks resonance when driven by trichotomous noise.