Hopf bifurcation of basic food web of species based on standard normal theory

Puyi Lam Kai-shek

Abstract

In this paper, we analyze the Hopf bifurcation of basic food web of four species based on standard normal form theory. The basic model we consider is owed to a bottom prey X, two competing predators Y and Z on X, and a super-predator W only on Y. It is found that periodic solutions arise from the main parameter values 1 and  through through a Hopf bifurcation point. The direction and type of the Hopf bifurcation involved as well as the parameter values also are determined.