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Allee-induced periodicity and bifurcations in a Gause-type model with interference phenomena

Author

Listed:
  • Gourav Mandal

    (Visva-Bharati)

  • Alejandro Rojas-Palma

    (Universidad Catolica del Maule)

  • Eduardo González-Olivares

    (Pontificia Universidad Catolica de Valparaiso)

  • Santabrata Chakravarty

    (Visva-Bharati)

  • Lakshmi Narayan Guin

    (Visva-Bharati)

Abstract

Predator–prey models currently serve as essential tools in the mathematical modelling of ecological systems, given their broad applicability in understanding complex interactions. This study examines the dynamics of a Gause-type predation model, incorporating assumptions that specialist predators compete for resources and that the prey population experiences an Allee effect. The model exhibits diverse dynamical behaviours through this ecological framework, including bi-stability, revealing the system’s intricate structure. The analysis highlights the existence of codimension one and codimension two bifurcations involving positive equilibria, such as saddle-node, Hopf, Bogdanov–Takens and Bautin bifurcations. The multifaceted dynamics of the system are further analysed across bi-parametric regions, represented through a variety of phase portraits. The ecological implications of these findings are discussed in detail to offer insights into the dynamic behaviours observed. Numerical simulations are also conducted to verify the analytical results, illustrating the model’s robustness and applicability. Graphic abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:98:y:2025:i:4:d:10.1140_epjb_s10051-025-00911-8
    DOI: 10.1140/epjb/s10051-025-00911-8
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    References listed on IDEAS

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    1. Eduardo González-Olivares & Javier Cabrera-Villegas & Fernando Córdova-Lepe & Alejandro Rojas-Palma, 2019. "Competition among Predators and Allee Effect on Prey, Their Influence on a Gause-Type Predation Model," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-19, March.
    2. 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.
    3. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.
    5. 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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