Stochastic resonance in an overdamped oscillator with frequency and input signal fluctuation

A linear oscillator subjected to multiplicative Gaussian white noise in both frequency and input signal fluctuation has been investigated in this paper. We mainly focus on the studies of the stochastic resonance(SR). Using the properties of Brownian motion and itô formula, we obtain the analytic expressions of both the first-order and second-order moment of the system’s stationary response. And the signal-to-noise ratio is introduced to analyze the influence of fluctuation in this system. It is worth mentioning that we solve the generalized Langevin equation with mathematical methods. Meanwhile, we discuss the variation of the output amplitude with the parameters of the system. We find that there is no SR in the first-order moment expression, while both SR and inverse stochastic resonance phenomena exist in the second-order moment expression, which have not been reported in the previous study.