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Globally Asymptotic Stability of a Delayed Integro-Differential Equation With Nonlocal Diffusion

Published online by Cambridge University Press:  20 November 2018

Peixuan Weng  and
Li Liu
Peixuan Weng
Affiliation:
School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China. e-mail: wengpx@scnu.edu.cn, liuli_0926@163.com
Li Liu
Affiliation:
School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China. e-mail: wengpx@scnu.edu.cn, liuli_0926@163.com
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Abstract

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We study a population model with nonlocal diffusion, which is a delayed integro-differential equation with double nonlinearity and two integrable kernels. By comparison method and analytical technique, we obtain globally asymptotic stability of the zero solution and the positive equilibrium. The results obtained reveal that the globally asymptotic stability only depends on the property of nonlinearity. As an application, we discuss an example for a population model with age structure.

Keywords

45J0535K5792D25integro-differential equationnonlocal diffusionequilibriumglobally asymptotic stabilitypopulation model with age structure
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 436 - 448
Copyright
Copyright © Canadian Mathematical Society 2017

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