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Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism

Author

Listed:
  • R. Lavanya
  • S. Vinoth
  • K. Sathiyanathan
  • Zeric Njitacke Tabekoueng
  • P. Hammachukiattikul
  • R. Vadivel

Abstract

In this article, we propose the Holling type‐II predator‐prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed model. Next, we also establish the local stability and Hopf bifurcation analysis for the corresponding delayed model. Finally, we discuss how cannibalism and delay play an important role in stabilizing and destabilizing the proposed system both theoretically and numerically.

Suggested Citation

  • R. Lavanya & S. Vinoth & K. Sathiyanathan & Zeric Njitacke Tabekoueng & P. Hammachukiattikul & R. Vadivel, 2022. "Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4071375
    DOI: 10.1155/2022/4071375
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    References listed on IDEAS

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    1. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    2. Vadivel, R. & Hammachukiattikul, P. & Gunasekaran, Nallappan & Saravanakumar, R. & Dutta, Hemen, 2021. "Strict dissipativity synchronization for delayed static neural networks: An event-triggered scheme," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. S. Vinoth & R. Sivasamy & K. Sathiyanathan & B. Unyong & R. Vadivel & Nallappan Gunasekaran, 2022. "A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population," Complexity, John Wiley & Sons, vol. 2022(1).
    4. S. Vinoth & R. Sivasamy & K. Sathiyanathan & B. Unyong & R. Vadivel & Nallappan Gunasekaran & C. Rajivganthi, 2022. "A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population," Complexity, Hindawi, vol. 2022, pages 1-21, March.
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    Cited by:

    1. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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