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Pattern formation of a diffusive predator–prey model with strong Allee effect and nonconstant death rate

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  • Yao, Shao-Wen
  • Ma, Zhan-Ping
  • Cheng, Zhi-Bo

Abstract

This paper is concerned with the pattern formation of a diffusive predator–prey model with strong Allee effect in the prey population and nonconstant death rate for the predator. The necessary and sufficient conditions of Turing instability are explicitly obtained. By regarding the diffusion coefficient d2 of the predator as bifurcation parameter, we demonstrate that at the critical value of the bifurcation parameter d2 a Turing bifurcation occurs (i.e. a pattern arises). The conditions for the stability of the pattern are also derived in detail. Our results show that strong Allee effect in our model plays a crucial role in the formation of stationary pattern, which is a strong contrast to the case without strong Allee effect.

Suggested Citation

  • Yao, Shao-Wen & Ma, Zhan-Ping & Cheng, Zhi-Bo, 2019. "Pattern formation of a diffusive predator–prey model with strong Allee effect and nonconstant death rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    • Handle: RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307964
    DOI: 10.1016/j.physa.2019.121350
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    Citations

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    Cited by:

    1. Xiangrui Li & Shuibo Huang, 2019. "Stability and Bifurcation for a Single-Species Model with Delay Weak Kernel and Constant Rate Harvesting," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    2. Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    3. Rana, Sourav & Bhattacharya, Sabyasachi & Samanta, Sudip, 2022. "Spatiotemporal dynamics of Leslie–Gower predator–prey model with Allee effect on both populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 32-49.

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