Stability and Bifurcations in Delayed Three-Species Model

Abstract

In this study, a system of delay differential equations arising from a three-species model with two predators feeding on a single prey is considered. It is assumed that the prey population grows logistically in the absence of predators, and both predator populations adapt a Holling type II functional response. Each response term includes a delay time, which reflects the gestation period of each predator. The predator equations are the same except for their delay time. The positive steady-state solution of the form (¯x, ¯y, ¯y) is called the symmetric equilibrium. This work examines the effects of the difference in the gestation period of the two predators. Conditions for the stability and bifurcations of the symmetric equilibrium for both cases when the delay times are equal and when one is larger than the other are provided.