Hopf Bifurcation for an Age-Structured Predator–Prey Model with Crowley–Martin Functional Response and Two Delays

Yajing Li ^[1] ; Zhihua Liu ^[1] ; Ziheng Zhang ^[2]
1. [1] Beijing Normal University
  
  Beijing Normal University
  
  China
2. [2] Tiangong University
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
Idioma: inglés
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Resumen
- In this paper, we investigate an age-structured predator–prey model with predatordependent functional response and two delays. The main feature of this article is to study the Crowley–Martin functional response, age structure and delays at the same time in a predator–prey model. We consider two time delays in this work: one is predator–prey reaction delay τ1 and the other one is predator maturation delay τ2 that appears in the fertility rate function. After transforming the original model into an abstract non-densely defined Cauchy problem and taking advantage of the integrated semigroup theory, we obtain the global existence and uniqueness of solutions, the existence of equilibria of the model. Then the global asymptotic stability of the boundary equilibrium is investigated under an appropriate condition. Furthermore, the existence of Hopf bifurcation at the positive equilibrium is established when τ1, τ2 are changed independently and simultaneously, as well as when τ1 = τ2. At last, numerical simulations are carried out to support the main theoretical results.