Complex dynamics of a three species prey-predator model with intraguild predation

Abstract

‘Omnivory’, a widespread mechanism in interacting populations, is defined as feeding on more than one trophic levels. In this work we have considered a three species model consisting of prey, intermediate predator that predates upon prey and top predator with intraguild predation. It is well known that intraguild predation destabilizes the food webs consisting of three and more trophic levels, and induces chaotic oscillation for Holling type-I functional response when the intensity of the intraguild predation becomes low. Here we have considered Holling type-II functional response between intermediate predator and intraguild predator and other functional responses are assumed to be linear. First we investigate local stability and bifurcation analysis of all axial and boundary equilibrium points. We observe two types of coexistence of three species - a steady-state coexistence and an oscillatory coexistence. Although it is difficult to find the analytical expressions for stability and bifurcation of the interior equilibrium point, we have verified numerically that a stable limit cycle bifurcates from the interior equilibrium point and ultimately chaos occurs via successive period doubling bifurcations. Bifurcation diagrams have been drawn with respect to all the system parameters to explore the complete dynamics of the model. Consideration of saturating functional response instead of law of mass action can suppress the chaotic oscillation leading to stable coexistence of three species at their steady-state.