Diffusion in a linear oscillator driven by colored noises with white cross-correlation

The diffusion in a linear oscillator driven by white cross-correlation colored noises in which one of the noises is modulated by a biased period signal is studied. Effects on d versus Q curve, d versus D curve, and d versus Ω curve by multiplicative colored noise self-correlation time τ1 as well as additive colored noise self-correlation time τ2 are revealed. Here d, Q, D, and Ω denote the diffusion coefficient of the oscillator, the intensity of the signal modulated noise, the intensity of the pure additive noise, and the signal frequency, respectively. It is found that a minimum exists in the d versus Q curve and the d versus D curve respectirely. The diffusion coefficient as a function of signal frequency Ω exhibits a pronounced maximum at Ω=Ω, here Ω　is the oscillator frequency. The condition of diffusion coefficient d=0 is derived.