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Analysis of a diffusive Leslie–Gower predator–prey model with nonmonotonic functional response

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  • Yin, Hongwei
  • Zhou, Jiaxing
  • Xiao, Xiaoyong
  • Wen, Xiaoqing

Abstract

In this paper, a diffusive Leslie–Gower predator–prey system with nonmonotonic functional respond is studied. We obtain the persistence of this model and show the local asymptotic stability of positive constant equilibrium by linearized analysis and the global stability by constructing Liapunov function. Besides, Turing instability of this equilibrium is obtained. The existence and nonexistence of positive nonconstant steady states of this model are established. Furthermore, by numerical simulations we illustrate the patterns of prey and predator.

Suggested Citation

  • Yin, Hongwei & Zhou, Jiaxing & Xiao, Xiaoyong & Wen, Xiaoqing, 2014. "Analysis of a diffusive Leslie–Gower predator–prey model with nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 51-61.
    • Handle: RePEc:eee:chsofr:v:65:y:2014:i:c:p:51-61
    DOI: 10.1016/j.chaos.2014.04.010
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    References listed on IDEAS

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    1. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
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    Cited by:

    1. Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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