Hopf bifurcation for a spatially and age structured population dynamics model

Zhihua Liu; Hui  Tang; Pierre  Magal

doi:10.3934/dcdsb.2015.20.1735

Article Contents

2015, Volume 20, Issue 6: 1735-1757. Doi: 10.3934/dcdsb.2015.20.1735

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Hopf bifurcation for a spatially and age structured population dynamics model

1.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875
2.
University of Bordeaux, IMB, UMR CNRS 5251, 33076 Bordeaux

Received: November 2013

Revised: February 2014

Published: August 2015

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Abstract

This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indicates that Hopf bifurcation occurs at a positive age/size dependent steady state of the model. The results are confirmed by some numerical simulations.

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Mathematics Subject Classification: 37L10, 37G15, 35B32, 35K55, 92D25.

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