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Order and Chaos in a Prey‐Predator Model Incorporating Refuge, Disease, and Harvesting

Author

Listed:
  • Dahlia Khaled Bahlool
  • Huda Abdul Satar
  • Hiba Abdullah Ibrahim

Abstract

In this paper, a mathematical model consisting of a prey‐predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type‐II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

Suggested Citation

  • Dahlia Khaled Bahlool & Huda Abdul Satar & Hiba Abdullah Ibrahim, 2020. "Order and Chaos in a Prey‐Predator Model Incorporating Refuge, Disease, and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:5373817
    DOI: 10.1155/2020/5373817
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    References listed on IDEAS

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    1. Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    2. Naji, Raid Kamel & Balasim, Alla Tariq, 2007. "Dynamical behavior of a three species food chain model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1853-1866.
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    Cited by:

    1. Rasha A. Ali & Hiba Abdullah Ibrahim, 2025. "Role of Wind and Fear on the Dynamic of a Prey and Two Competing Predators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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