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

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 nontrivial periodic orbit that bifurcates from the interior equilibrium when bifurcation parameter T crosses the bifurcation critical value To. 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. (C) 2019 Elsevier Ltd. All rights reserved.