Stability and bifurcation analysis of a tri-trophic food chain model with intraguild predation

Abstract

The dynamics of a three-component model for food web with intraguild predation is considered. The model is based on the collection of ordinary differential equations that describe the interactions among prey, intermediate predator and top predator. First, the model without self-limitation of the predators is studied. Boundedness of the system and existence of non-negative solutions are established. The local stability analysis of the equilibria is carried out to examine the behavior of the system. The possibility of Hopf bifurcation around non-negative equilibria with consumption rates as bifurcation parameters is studied. Center manifold theorem and the normal form theory are applied to obtain the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations support the analytical findings, which show that the extinction of one of the predators can occur under certain restrictions on the predation rate of the top predator. Subsequently, numerical analysis of the model with self-limitation of the predators is carried out. Simulations reveal that the system with intraspecific competition in the predator populations can reproduce coexistence between the three species in resource-rich environment.