Dynamical properties of a logistic growth model with cross-correlated noises

A logistic growth model driven by additive and multiplicative noises which are correlated with each other is investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution p_st(x), the relaxation time T_c, and the normalized correlation function C(s) of this system. The computational results show that the relaxation time T_c increases as the cross-correlated time τ increases, but decreases while the cross-correlated strength λ increases. The relationship between the relaxation time C(s) and the decay time s is given. Correlation time τ and correlation strength λ play an opposite role on dynamic properties in this logistic growth model.