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Hopf bifurcation in a diffusive predator-prey model with competitive interference

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  • Liu, Fuxiang
  • Yang, Ruizhi
  • Tang, Leiyu

Abstract

In this paper, we studied a diffusive predator-prey model with competitive interference and Crowley-Martin type functional response. The conditions for local stability of coexisting equilibrium are given by analyzing the eigenvalue spectrum. By using delay as bifurcation parameter, conditions for occurrence of Hopf bifurcation are also given. The property of bifurcating period solutions is investigated by calculating the normal form. Some numerical simulations are performed to support our theoretical result. Our conclusions show that diffusion and delay are two factors that should be considered in establishing the predator-prey model, since they can induce spatially bifurcating period solutions.

Suggested Citation

  • Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:250-258
    DOI: 10.1016/j.chaos.2019.01.029
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    References listed on IDEAS

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    1. Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    2. Huidong Cheng & Fang Wang & Tongqian Zhang, 2012. "Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, June.
    3. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    4. Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
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