Persistence and stability of a two prey one predator system

Abstract

The purpose of this work is to offer some mathematical analysis of the dynamics of a two prey one predator system in the presence of a time delay due to gestation. We derived criteria which guarantee the persistence of the three species and the global dynamics of the model system. Our study also shows that, the time delay may play a significant role on the stability of the system. Lastly, some numerical simulations are given to illustrate analytical results.

Keywords: Prey predator, persistence, extinction, global stability, Hopf bifurcation.