Hopf bifurcation of an age-structured prey–predator model with Holling type II functional response incorporating a prey refuge

Abstract

In this paper, an age-structured prey–predator model with Holling type II functional response incorporating a prey refuge is constructed. Through applying the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, we obtain that the model undergoes a Hopf bifurcation at the interior equilibrium which shows that this model has a non-trivial periodic orbit that bifurcates from the interior equilibrium when bifurcation parameter τ crosses the bifurcation critical value τ0. Numerical simulations are given to verify the theoretical analysis. The results manifest that the prey refuge has a stabilizing effect, namely, the prey refuge is a significant factor to maintain the balance between the prey population and the predator population.