MULTIPLE SCALE ANALYSIS OF A DELAYED PREDATOR PREY MODEL WITHIN RANDOM ENVIRONMENT

We consider a delayed predator prey model. The local stability and Hopf bifurcation results are stated taking the time delay as a control parameter. We apply multiple scale analysis to analyze the effects of additive white noises near the Hopf bifurcation point at the positive interior equilibrium state. The governing equations for the amplitude of oscillations on a slow time scale are derived. We identify the process of amplitude of oscillations and derive its transient properties. We show that oscillations, which would decay in the deterministic system whenever time delay lies below its critical value, persists for long time under the validity of multiple scale analysis.