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

Jorge Duarte (), Cristina Januário and Nuno Martins
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Jorge Duarte: ISEL-Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emidio Navarro 1, 1959-007 Lisboa, Portugal
Cristina Januário: ISEL-Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emidio Navarro 1, 1959-007 Lisboa, 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

Mathematics, 2025, vol. 13, issue 8, 1-16

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.

Keywords: chaos; tipping; delayed transitions; Hassell-type model; Allee effect (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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