Stochastic Resonance in a Fractional Oscillator with Cross-Correlation Noise

For an over-damped linear system with fractional derivative driven by both parametric excitation of colored noise and external excitaion of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we investigate the stochastic resonance phenomenon in this paper. Applying the Shapiro–Loginov formula and the generalized harmonic function approach, we obtain the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, the signal-to-noise ratio for the system is obtained. We find that the time-periodic modulation intensity between noises diversifies the stochastic resonance phenomenon and makes the system possess richer dynamic behaviors.