Bifurcation Control of a Delayed Predator–Prey System

In this paper, a delayed fractional-order predator–prey model with strong Allee effect and disease is studied. First, existence, uniqueness, non-negativity and the stability of the equilibrium points are discussed. The Hopf bifurcation condition with time delay as bifurcation parameter is given. Second, a delayed impulsive feedback controller is designed to control successfully the Hopf bifurcation. Finally, numerical simulations show that the disease can improve effectively the stability of the population under the Allee effect.