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Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey

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  • Kumar, Sachin
  • Kharbanda, Harsha

Abstract

We discuss the stability and bifurcation analysis of predator-prey model in the presence of group defense and non-linear harvesting in prey. Mathematically, we analyze the dynamics of the system such as boundedness of the solutions, existence and stability conditions of the equilibrium points. The model undergoes saddle-node, transcritical and Hopf-Andronov bifurcations. The direction of Hopf bifurcation by calculating the first Lyapunov number is examined. The effects of prey harvesting rate and death rate of predator on the model by considering them as bifurcation parameters are analyzed. In this paper, we dedicate ourselves to the investigation of the complex dynamics of the model to maintain the coexistence of the species which is important for ecological balance in the real environment. Several numerical simulations are performed to substantiate our analytical findings.

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  • Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:19-28
    DOI: 10.1016/j.chaos.2018.12.011
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
    4. Bulai, Iulia Martina & Venturino, Ezio, 2017. "Shape effects on herd behavior in ecological interacting population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 40-55.
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    Cited by:

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    2. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
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    4. Umar Sharif, Umi Syahirah Binti & Mohd, Mohd Hafiz, 2022. "Combined influences of environmental enrichment and harvesting mediate rich dynamics in an intraguild predation fishery system," Ecological Modelling, Elsevier, vol. 474(C).

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