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A Single Species Model with Impulsive Diffusion

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Abstract

In most models of population dynamics, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. In this paper we propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population, we prove that the map always has a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulation. Under impulsive diffusion the single species survives in the two patches.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China

    Jing Hui

  2. Computation Sciences, Guangxi University of Technology, Liuzhou 545006, China

    Jing Hui

  3. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China

    Lan-sun Chen

Authors
  1. Jing Hui
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  2. Lan-sun Chen
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Correspondence to Jing Hui.

Additional information

Supported by the National Natural Science Foundation of China (No.10171106)

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Hui, J., Chen, Ls. A Single Species Model with Impulsive Diffusion. Acta Mathematicae Applicatae Sinica, English Series 21, 43–48 (2005). https://doi.org/10.1007/s10255-005-0213-3

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  • DOI: https://doi.org/10.1007/s10255-005-0213-3

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