Hopf bifurcation for a predator–prey model with age structure

Dongxue Yan, Hui Cao, Xiaxia Xu and Xiaoqin Wang

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: This paper deals with a prey–predator model with age structure where the prey population is infected with pathogenic bacteria. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system. The criteria for global stability of two boundary equilibria are obtained. The criteria for local stability and instability of positive equilibrium is also discussed. Bifurcation analysis indicates that the predator–prey system with age structure exhibits bifurcation which is the main result of this paper. Finally, some numerical examples are provided to illustrate our obtained results.

Keywords: Age-structured model; C0-semigroup; Asymptotical stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119305461

DOI: 10.1016/j.physa.2019.04.189

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