Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

The diffusion in a harmonic oscillator driven by coloured noises \xi(t) and \eta(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time \tau_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient \lambda of the two Ornstein--Uhlenbeck (O-U) noises. 2) Changing the value of \tau_3, the curves of dversus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.