Stability and Hopf bifurcation analysis of a delayed predator-prey model with age-structure and Holling III functional response

摘要

This study investigates a delayed predator-prey model with age-structure and a Holling III response function. The considered model is first presented as an abstract Cauchy problem, then the criteria of the presence for the positive equilibrium point are gained. The global asymptotic stability of the boundary equilibrium and the local asymptotic stability of the positive equilibrium are examined, respectively, through detailed investigation of the location of the solutions for the model's characteristic equation. Then, using the Hopf bifurcation theorem, we show that Hopf bifurcation exists under certain criteria. At last, some numerical examples are performed to demonstrate the obtained theoretical results.

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