Bifurcation Analysis for Metapopulation Models

Two models with four components of chain populations are considered. In themodel, a prey population X is predated by individuals of a specialist predatorpopulation Y, and another prey population Z is predated by individuals of ageneralist predator population U. This model is governed by a system of fournonlinear first order ordinary differential equations. To study the dynamics of thefood chain model, the mentioned system of ordinary differential equations solvednumerically. One of the biological parameters varied in a sufficiently large rangeand its effects on the dynamics of the system are observed. Along the w - axis ofthe predating rate of the specialist predator Y, around four pointsw1=0.045, w2=0.088, w3=0.3000, and w4=0.920 we meet chaos. At eachtime chaos precedes period doublings.