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Multi-parameter bifurcations in a discrete Ricker-type predator–prey model with prey immigration

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  • Mokni, Karima
  • Mouhsine, Hajar
  • Ch-Chaoui, Mohamed

Abstract

This study examines a discrete-time prey–predator model featuring a Ricker-type growth function and immigration effects to uncover the dynamics shaping ecosystem stability. Through detailed bifurcation analysis, we identify codimension-one bifurcations, including transcritical, period-doubling, and Neimark–Sacker bifurcations, as well as codimension-two bifurcations involving 1:2, 1:3, and 1:4 resonances. Our results reveal that low immigration rates stabilize the system, ensuring predictable population dynamics, while exceeding critical thresholds induces complex behaviors, such as periodic oscillations and chaos. We numerically analyze the dynamics associated with 1:2, 1:3, and 1:4 resonances, utilizing two-parameter bifurcation diagrams and basins of attraction to illustrate the transitions and stability boundaries. These findings highlight the dual role of immigration in stabilizing and destabilizing ecosystems, offering valuable insights for ecological modeling, management, and conservation strategies.

Suggested Citation

  • Mokni, Karima & Mouhsine, Hajar & Ch-Chaoui, Mohamed, 2025. "Multi-parameter bifurcations in a discrete Ricker-type predator–prey model with prey immigration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 39-59.
    • Handle: RePEc:eee:matcom:v:233:y:2025:i:c:p:39-59
    DOI: 10.1016/j.matcom.2025.01.020
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    References listed on IDEAS

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    1. Mokni, Karima & Ch-Chaoui, Mohamed, 2024. "A Darwinian Beverton–Holt model with immigration effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 244-261.
    2. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Chou, Yen-hsi & Chow, Yunshyong & Hu, Xiaochuan & Jang, Sophia R.-J., 2021. "A Ricker–type predator–prey system with hunting cooperation in discrete time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 570-586.
    4. Yousef, A.M. & Rida, S.Z. & Ali, H.M. & Zaki, A.S., 2023. "Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Zhang, Limin & Zhang, Chaofeng & He, Zhirong, 2019. "Codimension-one and codimension-two bifurcations of a discrete predator–prey system with strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 155-178.
    6. Kumbhakar, Ruma & Hossain, Mainul & Karmakar, Sarbari & Pal, Nikhil, 2024. "An investigation of the parameter space in a tri-trophic food chain model with refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 37-59.
    7. Mokni, Karima & Ch-Chaoui, Mohamed & Mondal, Bapin & Ghosh, Uttam, 2024. "Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 992-1018.
    8. Mokni, Karima & Ali, Halima Ben & Ghosh, Bapan & Ch-Chaoui, Mohamed, 2025. "Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 789-813.
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    Cited by:

    1. Gourav Mandal & Alejandro Rojas-Palma & Eduardo González-Olivares & Santabrata Chakravarty & Lakshmi Narayan Guin, 2025. "Allee-induced periodicity and bifurcations in a Gause-type model with interference phenomena," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(4), pages 1-33, April.

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