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Steady-states of a Leslie–Gower model with diffusion and advection

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  • Qiu, Huanhuan
  • Guo, Shangjiang

Abstract

This paper focuses on a stationary Leslie–Gower model with diffusion and advection. Firstly, some existence conditions of nonconstant positive solutions are obtained by means of the Leray–Schauder degree theory. As diffusion and advection of one of the species both tend to infinity, we obtain a limiting system, which is a semi-linear elliptic equation with nonlocal constraint. In the simplified 1D case, the global bifurcation structure of nonconstant solutions of the limiting system is classified.

Suggested Citation

  • Qiu, Huanhuan & Guo, Shangjiang, 2019. "Steady-states of a Leslie–Gower model with diffusion and advection," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 695-709.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:695-709
    DOI: 10.1016/j.amc.2018.10.002
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    References listed on IDEAS

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    1. Na Zhang & Fengde Chen & Qianqian Su & Ting Wu, 2011. "Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-14, April.
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    Cited by:

    1. Li, Shangzhi & Guo, Shangjiang, 2021. "Permanence of a stochastic prey–predator model with a general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 308-336.

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