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 Omega curve by multiplicative colored noise self-correlation time tau(1) as well as additive colored noise self-correlation time tau(2) are revealed. Here d, Q, D, and Omega 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 Omega exhibits a pronounced maximum at Omega = (Omega) over tilde here (Omega) over tilde is the oscillator frequency. The condition of diffusion coefficient d = 0 is derived.