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Effect of density-dependent diffusion on a diffusive predator–prey model in spatially heterogeneous environment

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  • Zhang, Xuebing
  • An, Qi
  • Moussaoui, Ali

Abstract

The paper presents a class of predator–prey model with density-dependent diffusion in the spatially heterogeneous environment. We first provide the global existence and boundedness of the solution for the model. Then, by taking a variable transformation, the difficulty brought by the cross-diffusion can be overcome, and the existence, stability and local bifurcation of semi-trivial steady-state solutions for the equivalent system are further studied. Finally, the existence of positive solutions of the system is also given by using the Leray–Schauder degree theory and the method of principle eigenvalue, especially for the limit cases when the diffusion coefficient tends to zero or infinite.

Suggested Citation

  • Zhang, Xuebing & An, Qi & Moussaoui, Ali, 2025. "Effect of density-dependent diffusion on a diffusive predator–prey model in spatially heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 1-18.
    • Handle: RePEc:eee:matcom:v:227:y:2025:i:c:p:1-18
    DOI: 10.1016/j.matcom.2024.07.022
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    References listed on IDEAS

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    1. Biao Wang & Jianhua Wu, 2021. "Multiple positive steady states of a diffusive predator‐prey model in spatially heterogeneous environments," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 616-630, March.
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