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Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response

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  • Mortuja, Md Golam
  • Chaube, Mithilesh Kumar
  • Kumar, Santosh

Abstract

In this work, the dynamics of a predator-prey system considering square root type functional response for prey herd behaviour and nonlinear prey harvesting has been analyzed. The conditions under which all equilibria exist as well as the stability of every equilibrium point of the system have been investigated. The proposed model conditionally posses two types of bifurcations, Hopf bifurcation, and saddle-node bifurcation. The saddle-node bifurcation has been analyzed, where the bifurcation parameter is harvesting rate. The existence of a maximum sustainable yield to ensure both populations coexist has been discussed. The results give a clear idea that, if the harvesting rate is chosen at a proper value lesser than the maximum sustainable yield then both populations will coexist and the ecological balance will be maintained. The calculation of the first Lyapunov number provides the Hopf bifurcation direction. To verify our analytical results, several numerical simulations have been carried out.

Suggested Citation

  • Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921004252
    DOI: 10.1016/j.chaos.2021.111071
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    References listed on IDEAS

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    1. Ma, Xiangmin & Shao, Yuanfu & Wang, Zhen & Luo, Mengzhuo & Fang, Xianjia & Ju, Zhixiang, 2016. "An impulsive two-stage predator–prey model with stage-structure and square root functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 91-107.
    2. 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.
    3. Zhang, Lei & Wang, Wenjuan & Xue, Yakui, 2009. "Spatiotemporal complexity of a predator–prey system with constant harvest rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 38-46.
    4. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
    5. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
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    Cited by:

    1. Huangyu Guo & Jing Han & Guodong Zhang, 2023. "Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    2. Haiyin Li & Xuhua Cheng, 2021. "Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    3. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.

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