Work

Rate-induced phenomena in dynamical systems with attracting limit cycles

Year: 2025

Type: article

Abstract: We study the behavior of dynamical systems under a time-dependent change of an external parameter. We are interested in phenomena induced by the parameter changing sufficiently quickly, and we refer to these as rate-induced phenomena. We investigate such rate-induced phenomena in continuous-time planar dynamical systems, where the underlying fixed-parameter autonomous dynamics have limit cycles attractors, extending the work of Alkhayuon and Ashwin [Chaos 28(3), 033608 (2018)]. We discover new phenomena of rate-induced phase sensitivity, where the rate at which the parameter changes can trigger finite-time unpredictability in the dynamics. We also find that this new phenomenon interacts in an interesting way with the established notion of rate-induced tipping.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0251098

Authors: George Chappelle, Martin Rasmussen

Institution: Imperial College London

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Engineering and Physical Sciences Research Council

Awards: Attractors in random dynamical systems with bounded noise: persistence, resilience and bifurcations, EPSRC CENTRE FOR DOCTORAL TRAINING IN THE MATHEMATICS OF PLANET EARTH AT IMPERIAL COLLEGE LONDON AND THE UNIVERSITY OF READING, Applied Nonautonomous Dynamical Systems: Theory, Methods and Examples, Bifurcations of random dynamical systems with bounded noise