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Holling–Tanner model with Beddington–DeAngelis functional response and time delay introducing harvesting

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  • Roy, Banani
  • Roy, Sankar Kumar
  • Gurung, Dil Bahadur

Abstract

The paper is formulated with the Holling–Tanner prey–predator model with Beddington–DeAngelis functional response including prey harvesting. Gestational time delay of predator and the dynamic stability of time delay preventing system are incorporated into the system of our paper. The equilibria of the proposed system are determined and the existence of interior equilibrium point for the proposed system is described. Local stability of the system with the magnitude of time delay at the interior equilibrium point is discussed. Thereafter, the direction and the stability of Hopf bifurcation are established with the help of normal theory and center manifold theorem. Furthermore, profit function is calculated with the help of bionomic equilibrium and it is optimized using optimal control. Finally, some numerical simulations are introduced to verify the validity of analytic results of our proposed model.

Suggested Citation

  • Roy, Banani & Roy, Sankar Kumar & Gurung, Dil Bahadur, 2017. "Holling–Tanner model with Beddington–DeAngelis functional response and time delay introducing harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 1-14.
    • Handle: RePEc:eee:matcom:v:142:y:2017:i:c:p:1-14
    DOI: 10.1016/j.matcom.2017.03.010
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    References listed on IDEAS

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    1. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
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    Cited by:

    1. Ang, Tau Keong & Safuan, Hamizah M., 2019. "Harvesting in a toxicated intraguild predator–prey fishery model with variable carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 158-168.
    2. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.

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