Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology

J Dueñas; I P Longo; R Obaya

doi:10.1063/5.0159237

Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology

Chaos. 2023 Dec 1;33(12):123113. doi: 10.1063/5.0159237.

Authors

J Dueñas^{1

2}, I P Longo³, R Obaya^{1

2}

Affiliations

¹ Departamento de Matemática Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011 Valladolid, Spain.
² Instituto de Investigación en Matemáticas (IMUVa), Universidad de Valladolid, Paseo de Belén S/N, 47011 Valladolid, Spain.
³ Department of Mathematics, Imperial College London, 635 Huxley Building, 180 Queen's Gate South Kensington Campus, London SW7 2AZ, United Kingdom.

PMID: 38079649
DOI: 10.1063/5.0159237

Abstract

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution are efficient indicators (early-warning signals) of the presence of a tipping point. Precise time-dependent transitions with concave or d-concave variation in the state variable giving rise to scenarios of rate-induced tracking are shown. They are classified depending on the internal dynamics of the set of bounded solutions. Based on this classification, some representative features of these models are investigated by means of a careful numerical analysis.