Existence of positive periodic solutions for a predator-prey model

Abstract

In this paper, a class of nonlinear predator-prey models with three discrete delays is considered. By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system, two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays. Some numerical simulations are provided to illustrate our theoretical prediction.