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Impulsive diffusion in single species model

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  • Wang, Limin
  • Liu, Zhijun
  • Jinghui,
  • Chen, Lansun

Abstract

In most population models, 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 and a ϵ1−ϵ2 variation 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.

Suggested Citation

  • Wang, Limin & Liu, Zhijun & Jinghui, & Chen, Lansun, 2007. "Impulsive diffusion in single species model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1213-1219.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:4:p:1213-1219
    DOI: 10.1016/j.chaos.2006.01.102
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    Cited by:

    1. Jiao, Jianjun & Yang, Xiaosong & Cai, Shaohong & Chen, Lansun, 2009. "Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 522-532.
    2. Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    3. Xiangjun Dai & Hui Jiao & Jianjun Jiao & Qi Quan, 2023. "Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions," Mathematics, MDPI, vol. 11(18), pages 1-19, September.

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