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Bifurcations and simulations of two predator–prey models with nonlinear harvesting

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  • Lv, Yunfei
  • Pei, Yongzhen
  • Wang, Yong

Abstract

We propose and investigate a predator-prey model with selective nonlinear harvesting for the prey and predator, such harvesting increases smoothly to a limit value when the density of harvested population is large enough. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, limit cycle, heteroclinic and homoclinic orbit, bistability, saddle-node bifurcation, transcritical bifurcation, subcritical and supercritical Hopf bifurcation and Bogdanov–Takens bifurcation. Furthermore, some numerical simulations are given to illustrate these results.

Suggested Citation

  • Lv, Yunfei & Pei, Yongzhen & Wang, Yong, 2019. "Bifurcations and simulations of two predator–prey models with nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 158-170.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:158-170
    DOI: 10.1016/j.chaos.2018.12.038
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    References listed on IDEAS

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    1. Hu, Jiang-Hong & Xue, Ya-Kui & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2016. "Global dynamics of a predator–prey system modeling by metaphysiological approach," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 369-384.
    2. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
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    Cited by:

    1. Li, Wenjie & Guan, Yajuan & Cao, Jinde & Xu, Fei, 2024. "Global dynamics and threshold control of a discontinuous fishery ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Li, Xinxin & Yu, Hengguo & Dai, Chuanjun & Ma, Zengling & Wang, Qi & Zhao, Min, 2021. "Bifurcation analysis of a new aquatic ecological model with aggregation effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 75-96.
    3. Marick, Sounov & Bhattacharya, Santanu & Bairagi, Nandadulal, 2023. "Dynamic properties of a reaction–diffusion predator–prey model with nonlinear harvesting: A linear and weakly nonlinear analysis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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