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Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model

Author

Listed:
  • Hanaa Jamal Ahmed
  • Kawther Yusuf Abdulrahman
  • Karzan Abdulrahman Hamzah
  • Arkan Nawzad Mustafa

Abstract

This paper deals with dynamical analysis of an ecological model. This model includes two logistically growing prey species, namely, Prey X and Prey Y, and the third species Z behaves as the predator, predating both Prey X and Prey Y according to the extended Holling type‐II functional response. Furthermore, the effect of fear is incorporated in the growth rate of both species Prey X and Prey Y due to the predator Z. All the biologically possible steady state points are explored, and their local stability as well as global stability is analyzed based on the sample parameters. Next, we investigate the occurrence of local bifurcations around each steady state points by taking the value of the birth rate, death rate, and fear parameter as a bifurcation parameter. Finally, we perform extensive numerical simulations to support the evidence of our analytical results.

Suggested Citation

  • Hanaa Jamal Ahmed & Kawther Yusuf Abdulrahman & Karzan Abdulrahman Hamzah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:9391001
    DOI: 10.1155/ijmm/9391001
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    References listed on IDEAS

    as
    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).
    2. Junli Liu & Pan Lv & Bairu Liu & Tailei Zhang & Eulalia Martinez, 2021. "Dynamics of a Predator-Prey Model with Fear Effect and Time Delay," Complexity, Hindawi, vol. 2021, pages 1-16, April.
    3. 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, Hindawi, vol. 2025, pages 1-10, February.
    Full references (including those not matched with items on IDEAS)

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