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Allee effect in a diffusive predator–prey system with nonlocal prey competition

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  • Yang, Youwei
  • Wu, Daiyong
  • Shen, Chuansheng
  • Lu, Fengping

Abstract

Nonlocal competition and Allee effect have extensively been considered in modeling population dynamics of species independently. This paper introduces two aspects, which prey has nonlocal competition and predator is subject to Allee effect, in a predator–prey system to investigate the effects of predation on the spatial distribution of prey. The conditions for the coexistence equilibrium point to remain stable and to undergo spatially inhomogeneous Hopf bifurcation and Turing bifurcation have been studied. In the absence of Allee effect, we find that the coexistence equilibrium point of the system is locally asymptotically stable independent of the nonlocal competition. In the presence of Allee effect, nonlocal prey competition can destabilize the coexistence equilibrium point. Numerical simulations are carried out to illustrate the theoretical results. The amplitude of oscillation solution for nonlocal prey competition system is larger than local prey competition system until oscillation solution evolves to periodic solution. Also, nonlocal prey competition term can drive a spatially inhomogeneous Hopf bifurcation, and the spatially inhomogeneous periodic solution emerges. Moreover, it is showed that when the habitat domain is larger, comparing with local prey competition system, the prey diffusion coefficient of system with nonlocal prey competition needs to be larger for two species coexistence in the spatially homogeneous form.

Suggested Citation

  • Yang, Youwei & Wu, Daiyong & Shen, Chuansheng & Lu, Fengping, 2023. "Allee effect in a diffusive predator–prey system with nonlocal prey competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    • Handle: RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123001619
    DOI: 10.1016/j.physa.2023.128606
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    References listed on IDEAS

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    1. Merchant, Sandra M. & Nagata, Wayne, 2011. "Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition," Theoretical Population Biology, Elsevier, vol. 80(4), pages 289-297.
    2. Yang, Feng & Song, Yongli, 2022. "Stability and spatiotemporal dynamics of a diffusive predator–prey system with generalist predator and nonlocal intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 159-168.
    3. Peng, Yahong & Zhang, Guoying, 2020. "Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 366-378.
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    Cited by:

    1. Owolabi, Kolade M. & Jain, Sonal, 2023. "Spatial patterns through diffusion-driven instability in modified predator–prey models with chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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