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

Abstract

Puyi Lam Kai-shek

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.