Hopf bifurcation analysis of a predator–prey system with Holling type IV functional response and time delay

This paper is concerned with a predator–prey system with Holling type IV functional response and time delay. Our aim is to investigate how the time delay affects the dynamics of the predator–prey system. By choosing the delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are analyzed. Based on the normal form and the center manifold theory, the formulaes for determining the properties of Hopf bifurcation of the predator–prey system are derived. Finally, to support these theoretical results, some numerical simulations are given to illustrate the results.