Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13081275

Authors: Jorge Duarte, Cristina Januário, Nuno Martins

Institutions: University of Lisbon, Universidade Politécnica de Lisboa, Instituto Superior Técnico, Centro de Análise Matemática Geometria e Sistemas Dinâmicos, University of Aveiro

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Center for Research and Development in Mathematics and Applications