Hopf bifurcation in a predator–prey system with discrete and distributed delays

In this paper, a predator–prey system with discrete and distributed delays is considered. By regarding the delay as the bifurcation parameter and analyzing the associated characteristic equation of the original system at the positive equilibrium, it is found that Hopf bifurcations occur when the delay passes through a certain critical value. Finally, numerical simulations are given to support our theoretical results.