Influences of time delay on logistic growth process driven by colored correlated noises

Abstract

The small time-delay approach is applied to logistic growth model when time-delayed feedback and colored correlated noises are included in the system. The steady state probability distribution Pst(x) of the tumor cell number is obtained. It is found that a configuration transition of multiple peaks to a single peak occurs due to the variation of delay time τ. An extremum appears in the curves of the mean of the steady-state tumor cell number 〈x〉, the second moment 〈x2〉, and the normalized variance Var versus λ. The positions and the peak values of the extrema can be effected by the time delay.