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Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis

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  • Luo, Demou

Abstract

The aim of this study is to establish a precise illustration of the structure of the nonconstant steady state for a Holling-II predator–prey reaction–diffusion system, with prey-taxis. We treat the nonlinear prey-taxis as a bifurcation parameter to discuss the global bifurcation of the system. Furthermore, the prey-taxis term, under a rather natural condition, offers nonconstant steady states. In the proof, a priori estimates and the regularity of the steady states will play an important role. Numerical simulation is provided to support our main theoretical results. Finally, conclusions are drawn to summarise the main analytical results.

Suggested Citation

  • Luo, Demou, 2021. "Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003295
    DOI: 10.1016/j.chaos.2021.110975
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    References listed on IDEAS

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    1. Abbas, Syed & Tripathi, Jai Prakash & Neha, A.A., 2017. "Dynamical analysis of a model of social behavior: Criminal vs non-criminal population," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 121-129.
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    Cited by:

    1. Wu, Daiyong & Yang, Youwei & Wu, Peng, 2023. "Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 283-300.
    2. Yimamu Maimaiti & Wang Zhang & Ahmadjan Muhammadhaji, 2023. "Stationary Pattern and Global Bifurcation for a Predator–Prey Model with Prey-Taxis and General Class of Functional Responses," Mathematics, MDPI, vol. 11(22), pages 1-21, November.

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