IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i8p1275-d1633601.html
   My bibliography  Save this article

On Chaos, Tipping and Delayed Dynamical Transitions in a Hassell-Type Population Model with an Allee Effect

Author

Listed:
  • Jorge Duarte

    (ISEL-Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emidio Navarro 1, 1959-007 Lisboa, Portugal
    Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal)

  • Cristina Januário

    (ISEL-Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emidio Navarro 1, 1959-007 Lisboa, Portugal
    Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

  • Nuno Martins

    (Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
    Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal)

Abstract

This study examines abrupt changes in system dynamics, focusing on a Hassell-type density-dependent model with an Allee effect. It aims to analyze tipping points leading to extinction and bistability, including chaotic dynamics. Key methods include computing the topological entropy and Lyapunov exponents when varying the carrying capacity, the intrinsic growth rate and the initial conditions, providing a detailed characterization of chaotic regimes. Meanwhile, we derive an inverse square-root scaling law near a saddle-node bifurcation using a complex analysis. This study uniquely integrates chaos theory, a bifurcation analysis and scaling laws into a density-dependent ecological model with an Allee effect, revealing how chaotic regimes, bistability and an analytically derived inverse square-root scaling law near extinction shape the tipping point dynamics and critical transitions in ecological systems.

Suggested Citation

  • Jorge Duarte & Cristina Januário & Nuno Martins, 2025. "On Chaos, Tipping and Delayed Dynamical Transitions in a Hassell-Type Population Model with an Allee Effect," Mathematics, MDPI, vol. 13(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1275-:d:1633601
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/8/1275/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/8/1275/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1275-:d:1633601. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.