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Stationary Pattern and Global Bifurcation for a Predator–Prey Model with Prey-Taxis and General Class of Functional Responses

Author

Listed:
  • Yimamu Maimaiti

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

  • Wang Zhang

    (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China)

  • Ahmadjan Muhammadhaji

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
    The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

Abstract

This paper will explore a predator–prey model that incorporates prey-taxis and a general functional response in a bounded domain. Firstly, we will examine the stability and pattern formation of both local and nonlocal models. Our main finding is that the inclusion of nonlocal terms enhances linear stability, and the system can generate patterns due to the effects of prey-taxis. Secondly, we consider the nonlinear prey-taxis as the bifurcation parameter in order to analyze the global bifurcation of this model. Specifically, we identify a branch of nonconstant solutions that emerges from the positive constant solution when the prey-tactic sensitivity is repulsive. Finally, we will validate the effectiveness of the theoretical conclusions using numerical simulation methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4641-:d:1279775
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    References listed on IDEAS

    as
    1. Yang, Feng & Song, Yongli, 2022. "Stability and spatiotemporal dynamics of a diffusive predator–prey system with generalist predator and nonlocal intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 159-168.
    2. Yan, Xiao & Maimaiti, Yimamu & Yang, Wenbin, 2022. "Stationary pattern and bifurcation of a Leslie–Gower predator–prey model with prey-taxis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 163-192.
    3. 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).
    Full references (including those not matched with items on IDEAS)

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