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Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration

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  • Mokni, Karima
  • Ali, Halima Ben
  • Ghosh, Bapan
  • Ch-Chaoui, Mohamed

Abstract

In this paper, we investigate the complex dynamics of a Darwinian Ricker system through a comprehensive qualitative and dynamical analysis. Our research shows that the system exhibits Neimark–Sacker bifurcation, period-doubling bifurcation, and codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. These findings are derived using bifurcation and center manifold theories. We numerically illustrate all bifurcation results and chaotic features, providing a thorough understanding of the system’s behavior. This detailed examination of the Darwinian Ricker system, with a focus on the interplay between immigration and the strong Allee effect, enhances our understanding of the intricate mechanisms driving population dynamics. Furthermore, it highlights the significant implications for ecological modeling, particularly in predicting ecosystem responses to external perturbations such as climate change and species invasions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:789-813
    DOI: 10.1016/j.matcom.2024.10.017
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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. 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.
    3. 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).
    4. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(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. 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.
    7. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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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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