Modeling and numerical simulations for a prey–predator model with interference among predators

Abstract

In this paper, we modeled a prey–predator system with interference among predators using the Crowley–Martin functional response. The local stability and existence of Hopf bifurcation at the coexistence equilibrium of the system in the absence of diffusion are analyzed. Further, the stability of bifurcating periodic solutions is investigated. We derived the conditions for which nontrivial equilibrium is globally asymptotically stable. In addition, we study the diffusion driven instability, Hopf bifurcation of the corresponding diffusion system with zero flux boundary conditions and the Turing instability region regarding parameters are established. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical simulations are performed to illustrate the theoretical results.