Bifurcation analysis of an intraguild predator-prey model

This paper deals with a predator-prey model and a modified version consisting of a resource-consumer with two consumer species. We analyze the stability of equilibria and for the interior equilibrium, we show that the system undergoes some generic bifurcations such as fold, Hopf and Hopf-zero bifurcations. We characterize these bifurcations by the center manifold theorem and the normal form theory. We further compute the critical normal form coefficients of the reduced system to the center manifold and conclude the non-degeneracy conditions for the computed bifurcations. By using the numerical continuation method, we compute several bifurcation curves emanating from the detected bifurcation points to examine the obtained analytical results as well as to reveal further complex dynamical behaviors of the system which can not be achieved analytically. Especially for both the original and modified models on the Hopf bifurcation curve, we detect some codimension two bifurcations namely Hopf-zero and generalized Hopf.