On the Bifurcation Pattern and Normal Form in a Modified Predator–Prey Nonlinear System

Abstract

Detailed bifurcation pattern and stability structure is studied in a modified predator–prey system, with nonmonotonic response function. It is observed that almost all the parameters of the system have a positive influence as far as bifurcation is concerned. The analysis is done with the help of the package MATCONT. In the second stage of the analysis the detailed structure of the normal form is obtained after the corresponding position of Hopf bifurcation and Bogdanov–Takens bifurcation are identified with the help of a modified approach recently proposed by Kuznetsov (1995, Elements of Bifurcation Theory, Springer, New York, Chap. 8). It is important to note that the positions of Hopf and Bogdanov–Taken bifurcation as obtained from the analytic studies in this approach coincides exactly with those obtained from MATCONT.