Effects of Cross-Correlation Colour Noises on Tumour Growth Process

We present a tumour cell growth process model including a multiplicative coloured noise and an additive coloured noise correlated. How the noise cross-correlation intensity λ and correlation time τ can affect the steady state properties of tumour cell growth model are discussed by solving an approximative Fokker--Planck equation. It is found that the increase of noise correlation time τ can cause the tumour cell number increasing, but the increase of multiplicative noise intensity can cause the tumour cell number extinction. We also find that the increase of cross-correlation intensity λ in the case of 0 <λ<1 can cause the tumour cell number extinction, whereas increase of cross-correlation intensity λ in the case of λ < 0 can cause the tumour cell number increasing.