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Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator

Author

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  • Xiaoqin Wang
  • Yongli Cai
  • Huihai Ma

Abstract

The reaction-diffusion Holling-Tanner prey-predator model considering the Allee effect on predator, under zero-flux boundary conditions, is discussed. Some properties of the solutions, such as dissipation and persistence, are obtained. Local and global stability of the positive equilibrium and Turing instability are studied. With the help of the numerical simulations, the rich Turing patterns, including holes, stripes, and spots patterns, are obtained.

Suggested Citation

  • Xiaoqin Wang & Yongli Cai & Huihai Ma, 2013. "Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, February.
    • Handle: RePEc:hin:jnddns:984960
    DOI: 10.1155/2013/984960
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    Cited by:

    1. Junbo Jia & Pan Yang & Huaiping Zhu & Zhen Jin & Jinqiao Duan & Xinchu Fu, 2023. "Planar Bistable Structures Detection via the Conley Index and Applications to Biological Systems," Mathematics, MDPI, vol. 11(19), pages 1-25, September.
    2. 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.
    3. Li, Xiaoshuang & Pang, Danfeng & Wallhead, Philip & Bellerby, Richard Garth James, 2023. "Dynamics of an aquatic diffusive predator–prey model with double Allee effect and pH-dependent capture rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.

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