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Hopf bifurcation for a predator–prey model with age structure

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  • Yan, Dongxue
  • Cao, Hui
  • Xu, Xiaxia
  • Wang, Xiaoqin

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.

Suggested Citation

  • Yan, Dongxue & Cao, Hui & Xu, Xiaxia & Wang, Xiaoqin, 2019. "Hopf bifurcation for a predator–prey model with age structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    • Handle: RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119305461
    DOI: 10.1016/j.physa.2019.04.189
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