DYNAMICAL PROPERTIES OF AN ANTI-TUMOR CELL GROWTH SYSTEM IN THE PRESENCE OF DELAY AND CORRELATED NOISES

Abstract

We study dynamical properties of an anti-tumor cell growth system in the presence of time delay and correlations between multiplicative and additive white noise. Using the small time delay approximation, the Novikov theorem and Fox approach, the stationary probability distribution (SPD) is obtained. Based on the SPD, the expressions of the normalized correlation function C(s) and the associated relaxation time Tc are derived by means of Stratonovich decoupling ansatz. Based on numerical computations, we find the following: (i) The SPD exhibits one-peak → two-peaks → one-peak phase transitions as the correlation intensity λ varies. (ii) The relaxation time Tc exhibits a one-peak structure for negatively correlated noise (λ<0), however for positively correlated noise (λ>0), the relaxation time Tc decreases monotonously. (iii) The effects of the delay time τ on Tc and C(s) are entirely the same for λ<0 and for λ>0, i.e. τ enhances the fluctuation decay of the population of tumor cells.