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 pst(x)pst(x), the relaxation time TcTc, and the normalized correlation function C(s)C(s) of this system. The computational results show that the relaxation time TcTc increases as the cross-correlated time ττ increases, but decreases while the cross-correlated strength λλ increases. The relationship between the relaxation time C(s)C(s) and the decay time ss is given. Correlation time ττ and correlation strength λλ play an opposite role on dynamic properties in this logistic growth model.