Dynamics of a model three species predator-prey system with choice.

摘要

Studies of predator-prey systems vary from simple Lotka-Volterra type to nonlinear systems involving the Holling Type II or Honing Type III functional response functions. Some systems are modeled to represent a simple food chain, while others involve mutualism, competition and even switching of predator-prey roles. In this study, we investigate the dynamics of a three species system in which the principle predator has a choice of two prey, while the prey species change their behavior from being prey to predator and vice versa.; Biological and mathematical conditions for the existence of equilibria and local stability are given. A proof to show the nonexistence of periodic solutions in the corresponding two species system is also given. Global stability of the coexistence equilibrium in the top predator-prey system is demonstrated through numerical simulations. The resulting quintic polynomial through full symmetry analysis provide for conditions for a cusp bifurcation using resultants theory. Various numerical simulations to illustrate the population dynamics of the corresponding two species system as well as the three species system model are given.