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Qualitative analysis for a diffusive predator–prey model with hunting cooperative

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  • Wu, Daiyong
  • Zhao, Min

Abstract

This paper investigates a predator–prey model that adds a cooperation term to the attack rate of the predator population. For the non-spatial model, the existence and stability of non-negative equilibrium points, and bifurcations are studied by choosing cooperation coefficient as control parameter. Our analytical results show that hunting cooperation can be beneficial to the predator population. However, as the cooperation coefficient increases, hunting cooperation can also destabilize the model and promote a sudden collapse of the predator population. For the spatial model, the stability of positive constant steady state solution, Hopf bifurcation and Turing instability are discussed. It is obtained that when the predation diffusion is not smaller than the prey diffusion, the spatial model can reserve the stable stability of the positive constant steady state solution. It is noted that the model without hunting cooperative does not generate Turing instability, while the model with hunting cooperative may generate Turing instability.

Suggested Citation

  • Wu, Daiyong & Zhao, Min, 2019. "Qualitative analysis for a diffusive predator–prey model with hunting cooperative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 299-309.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:299-309
    DOI: 10.1016/j.physa.2018.09.176
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    References listed on IDEAS

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    1. Abernethy, Gavin M. & Mullan, Rory & Glass, David H. & McCartney, Mark, 2017. "A multiple phenotype predator–prey model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 762-774.
    2. Camara, B.I. & Haque, M. & Mokrani, H., 2016. "Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 374-383.
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    Cited by:

    1. Han, Renji & Dey, Subrata & Banerjee, Malay, 2023. "Spatio-temporal pattern selection in a prey–predator model with hunting cooperation and Allee effect in prey," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Yanfei Du & Ben Niu & Junjie Wei, 2021. "Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect," Mathematics, MDPI, vol. 9(24), pages 1-40, December.
    3. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    4. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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