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

Shengqin Xu; Chuncheng Wang; Dejun Fan

doi:10.3934/dcdsb.2018264

Article Contents

2019, Volume 24, Issue 6: 2535-2549. Doi: 10.3934/dcdsb.2018264

This issue Previous Article Global eradication for spatially structured populations by regional control Next Article On the long-time behaviour of age and trait structured population dynamics

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
* Corresponding authors

Received: November 2017

Revised: May 2018

Early access: October 2018

Published: June 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B32; Secondary: 92D30.

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Figure 1. A solution of (1) that tends to the positive steady states when $\tau = 3.5 < \tau_0$

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Figure 2. For $\tau = 6>\tau_0$, the solution will oscillate periodically

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