Bifurcation Analysis for Metapopulation Models

Abstract

Two models with four components of chain populations are considered. In the model, a prey population X is predated by individuals of a specialist predator population Y, and another prey population Z is predated by individuals of a generalist predator population U. This model is governed by a system of four nonlinear first order ordinary differential equations. To study the dynamics of the food chain model, the mentioned system of ordinary differential equations solved numerically. One of the biological parameters varied in a sufficiently large range and its effects on the dynamics of the system are observed.  Along the axis of the predating rate of the specialist predator, around four points  we meet chaos. At each time chaos precedes period doublings.