Local Stability and Hopf Bifurcation Analysis for a Predator-Prey control Model with Two Delays

Abstract

Based on facts of time delay will influence dynamical behavior and control theory is more appropriate to reflect the natural rule, constructed a predator-prey control model with two delays,choose the two delays as the bifurcation parameter,according to the Routh-Hurwize discriminant method,we studied the local stability and Hopf branch of the control system.The sufficient conditions for the local stability and the existence of Hopf bifurcation are established.Finally,the effectiveness of the controller is verified by numerical simulation.