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Qualitative Analysis of a Spatiotemporal Prey‐Predator Model with Additive Allee Effect and Fear Effect

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  • Changcheng Ke
  • Ming Yi
  • Yanfeng Guo

Abstract

A diffusive predator‐prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non‐negative and non‐trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non‐constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non‐negative constant solutions. The spatially homogeneous and non‐homogeneous periodic solutions, as well as non‐constant steady state solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results.

Suggested Citation

  • Changcheng Ke & Ming Yi & Yanfeng Guo, 2022. "Qualitative Analysis of a Spatiotemporal Prey‐Predator Model with Additive Allee Effect and Fear Effect," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:5715922
    DOI: 10.1155/2022/5715922
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    1. Liyun Lai & Zhenliang Zhu & Fengde Chen, 2020. "Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect," Mathematics, MDPI, vol. 8(8), pages 1-21, August.
    2. Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar, 2021. "Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Pal, Pallav Jyoti & Saha, Tapan, 2015. "Qualitative analysis of a predator–prey system with double Allee effect in prey," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 36-63.
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