Existence of a Limit Cycle in an Intraguild Food Web Model with Holling Type II and Logistic Growth for the Common Prey

Abstract

In this paper , we prove the existence of a limit cycle for a given system of differential equations corresponding to an asymmetrical intraguild food web model with functional responses Holling type II for the middle and top pr edators and logistic grow for the (common) prey. The existence of such limit cycle is guaranteed, via the first Lyapunov coefficient and the Andronov- Hopf bifurcation theorem, under certain cond itions for the parameters involved in the system.