Hopf bifurcation for a predator–prey model with age structure

•Consider a predator–prey model with age structure.•Rewrite the age structured model as a non-densely defined Cauchy problem.•The stability and Hopf bifurcation are studied.•The numerical simulations support our results.

A predator–prey model is investigated in which the predator population is assumed to have an age structure. We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness of positive age-dependent equilibrium for the model. Bifurcation analysis indicates that the predator–prey system with age structure exhibits Hopf bifurcation which is the main result of this paper. Numerical simulations are given to illustrate the given results.