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

  Published:2017-02-28
 Printed: Jun 2017
  • Peixuan Weng,
    School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China
  • Li Liu,
    School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China
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Abstract

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 application, an example for a population model with age structure is discussed at the end of the article.
Keywords: integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure
MSC Classifications: 45J05, 35K57, 92D25 show english descriptions Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
Reaction-diffusion equations
Population dynamics (general)
45J05 - Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
35K57 - Reaction-diffusion equations
92D25 - Population dynamics (general)
 

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