Rate-induced phenomena in dynamical systems with attracting limit cycles
File(s)
Published version
Author(s)
Chappelle, George
Rasmussen, Martin
Type
Journal Article
Abstract
We study the behaviour 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 [1]. We discover
a 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.
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 [1]. We discover
a 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.
Date Issued
2025-07-01
Date Acceptance
2025-06-02
Citation
Chaos: an interdisciplinary journal of nonlinear science, 2025, 35 (7)
ISSN
1054-1500
Publisher
American Institute of Physics
Journal / Book Title
Chaos: an interdisciplinary journal of nonlinear science
Volume
35
Issue
7
Copyright Statement
© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
073113
Date Publish Online
2025-07-07