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Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition

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  • Peng, Yahong
  • Zhang, Guoying

Abstract

Nonlocal reaction–diffusion model is an important area to study the dynamics of the individuals which compete for resources. In this paper, we consider a predator–prey model with herd behavior and nonlocal prey competition. We investigate the effects of nonlocal competition on dynamics of the system in the bounded region when the kernel function takes 1|Ω| and derive the conditions that the nonlocal system undergoes Hopf bifurcation and Turing bifurcation. Then we discuss the influence of nonlocal competition on the stability of the positive constant equilibrium in unbounded region when the kernel function takes a step kernel function. Our result shows that nonlocal competition can destabilize the stability of the predator–prey system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:366-378
    DOI: 10.1016/j.matcom.2019.11.012
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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. Peng, Yahong & Ling, Heyang, 2018. "Pattern formation in a ratio-dependent predator-prey model with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 307-318.
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    Cited by:

    1. Shi, Qingyan & Song, Yongli, 2022. "Spatiotemporal pattern formation in a pollen tube model with nonlocal effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    3. 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).
    4. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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