Abstract: 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.

Key words: coloured cross-correlation, cross-correlation coefficient, diffusion coefficient, signal modulated noise, noise-induced transition