Dynamics of Two Preys - One Predator System with Competition between Preys

Abstract

We study the dynamics of two preys - one predator interaction with competition between prey populations. The proposed model is developed from the Lotka-Volterra predator-prey model. We first discuss some fundamental issues such as equilibrium points and the stability of each equilibrium point. The analysis shows that there are seven equilibrium points and some of them are conditionally locally asymptotically stable. The dynamical behavior of the proposed model is then verified numerically. We also observe numerically the occurrence of bistability, as well as a Hopf bifurcation which is driven by the conversion rate of predation into the predator growth rate.