Stability analysis for a size-structured juvenile-adult population model

Xianlong Fu; Dongmei Zhu

doi:10.3934/dcdsb.2014.19.391

Article Contents

2014, Volume 19, Issue 2: 391-417. Doi: 10.3934/dcdsb.2014.19.391

This issue Previous Article Nonlocal convection-diffusion volume-constrained problems and jump processes Next Article Hyperbolic quenching problem with damping in the micro-electro mechanical system device

Stability analysis for a size-structured juvenile-adult population model

Xianlong Fu^1, and
Dongmei Zhu^1,

1.
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241

Received: March 31, 2013

Revised: September 30, 2013

Published: February 2014

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Abstract

In this paper, we discuss the asymptotic behavior of a size-structured juvenile-adult population equation with resource-dependent and delayed birth process. The linearization about stationary solutions is analyzed by using semigroup and spectral methods. The juvenile-adult interaction, resource-dependent and delayed boundary condition are considered deliberately for the system to investigate their influences on the asymptotic behavior of solutions. We obtain the stability and instability of the stationary solutions by given some biologically meaningful conditions in two important cases. Finally, two examples are presented and simulated to illustrate the obtained results.

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Mathematics Subject Classification: 34G20, 92D25, 34D20, 35F30.

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