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Turing patterns in a predator–prey model with double Allee effect

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  • Wang, Fatao
  • Yang, Ruizhi
  • Zhang, Xin

Abstract

In this paper, a predator–prey model with double Allee effect and self-diffusion terms is considered. The stability of the coexisting equilibrium is studied by analyzing the eigenvalue spectrum, and the spatial Turing patterns are investigated by using the method of multiple scale analysis. The amplitude equation is obtained, which shows that the system supports patterns like spots, stripes, hexagonal patterns and mixed-mode patterns. The influence of double Allee effect in system is discussed by the comparison of bifurcation diagrams. Finally, the numerical simulations have verified the correctness of above theoretical analysis and tell how the double Allee effect plays an important role in biological universe.

Suggested Citation

  • Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:170-191
    DOI: 10.1016/j.matcom.2024.01.015
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    References listed on IDEAS

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    1. Wang, Fatao & Yang, Ruizhi, 2023. "Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Gambino, G. & Lombardo, M.C. & Sammartino, M., 2012. "Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1112-1132.
    3. Wang, Jin-Shan & Wu, Yong-Ping & Li, Li & Sun, Gui-Quan, 2020. "Effect of mobility and predator switching on the dynamical behavior of a predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
    5. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
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    1. Pal, Pallav Jyoti & Mandal, Gourav & Guin, Lakshmi Narayan & Saha, Tapan, 2024. "Allee effect and hunting-induced bifurcation inquisition and pattern formation in a modified Leslie–Gower interacting species system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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