Asymptotic analysis for an age-structured predator–prey model with Beddington–Deangelis functional response

Abstract

This paper focuses on the asymptotic behavior of an age-structured predator–prey model with Beddington–Deangelis functional response and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Then, the global asymptotic stability of the boundary equilibrium is successfully established by determining the distribution of eigenvalues. Hopf bifurcation results with two parameters are also well described under some conditions by the method of stability switching curves. Finally, some numerical examples are presented to further deepen the understanding of the obtained results.