Hopf bifurcation in an age-structured population model with two delays

Xianlong Fu; Zhihua Liu; Pierre Magal

doi:10.3934/cpaa.2015.14.657

Article Contents

2015, Volume 14, Issue 2: 657-676. Doi: 10.3934/cpaa.2015.14.657

This issue Previous Article Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain Next Article Refined blow-up results for nonlinear fourth order differential equations

Hopf bifurcation in an age-structured population model with two delays

1.
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241
2.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875
3.
Institut de Mathématiques de Bordeaux, UMR CNRS 5251, INRIA Bordeaux sud-ouest, EPI Anubis, UFR Sciences de la Vie, Université Victor Segalen Bordeaux 2, 3 ter Place de la Victoire, 33076 Bordeaux

Received: February 28, 2014

Revised: July 31, 2014

Published: February 2015

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Abstract

This paper is devoted to the study of an age-structured population system with Riker type birth function. Two time lag factors is considered for the model. One lag lies in the birth process and the another is in the birth function. We investigate some dynamical properties of the equation by using integrated semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system. The obtained results show how the two delays affect these dynamical properties.

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Mathematics Subject Classification: 34G20, 37G15, 35B32, 35K55, 92D25.

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