Collective Behaviors of Star-Coupled Harmonic Oscillators with Fluctuating Frequency in the Presence of Stochastic Resonance

Abstract

The stochastic resonance (SR) of a star-coupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media is studied. The multiplicative noise is modeled as a dichotomous noise and the memory of viscous media is characterized by a fractional power kernel function. By using the Shapiro–Loginov formula and Laplace transform, we obtain the analytical expressions of the first moment of the steady-state response and study the relationship between the system response and the system parameters in the long-time limit. The simulation results show the nonmonotonic dependence between the response output gain and the input signal frequency, the noise parameters of the system, etc., which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the fluctuation noise, the number of particles, and the fractional order work together, producing more complex dynamic phenomena compared with the integral-order system. In addition, all the theoretical analyses are supported by the corresponding numerical simulations. We believe that the results that we have found may be a certain reference value for the research and development of the SR.