Effects of time-delay in stationary properties of a logistic growth model with correlated noises

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉st ) and normalized variance λ2 of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ ) enhances the coherence resonance in 〈x〉st as a function of the multiplicative noise intensity (D) and increases 〈x〉st as a function of the additive noise intensity (α), i.e., τ enhances fluctuation of the system, however, the strength (λ) of correlations between multiplicative and additive noise plays a contrary role to τ on these; (ii) τ enhances the coherence resonance in κ as a function ofD and increases κ as a function of α, i.e., τ speeds up the rate of state transition, however, λ also plays a contrary role to τ on these. © 2009 Elsevier B.V. All rights reserved.