# American Institute of Mathematical Sciences

June  2019, 24(6): 2535-2549. doi: 10.3934/dcdsb.2018264

## Stability and bifurcation in an age-structured model with stocking rate and time delays

 1 Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China 2 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

* Corresponding authors

Received  November 2017 Revised  May 2018 Published  October 2018

In this paper, a predator-prey model with age structure, stocking rate and two delays is investigated. We show that Hopf bifurcation occurs when one of the time delay $τ$ crosses a sequence of critical values, by applyingHopf bifurcation theory for abstract Cauchy problems with non-dense domain. Numerical simulations are included to verify our results and a summary is also given.

Citation: Shengqin Xu, Chuncheng Wang, Dejun Fan. Stability and bifurcation in an age-structured model with stocking rate and time delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2535-2549. doi: 10.3934/dcdsb.2018264
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##### References:
A solution of (1) that tends to the positive steady states when $\tau = 3.5 < \tau_0$
For $\tau = 6>\tau_0$, the solution will oscillate periodically
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