Stabilization of cyclic processes by slowly varying forcing

Newman, J. and Lucas, M. and Stefanovska, A. (2021) Stabilization of cyclic processes by slowly varying forcing. Chaos, 31 (12). ISSN 1089-7682

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Abstract

We introduce a new mathematical framework for the qualitative analysis of dynamical stability, designed particularly for finite-time processes subject to slow-timescale external influences. In particular, our approach is to treat finite-time dynamical systems in terms of a slow-fast formalism in which the slow time only exists in a bounded interval, and consider stability in the singular limit. Applying this to one-dimensional phase dynamics, we provide stability definitions somewhat analogous to the classical infinite-time definitions associated with Aleksandr Lyapunov. With this, we mathematically formalize and generalize a phase-stabilization phenomenon previously described in the physics literature for which the classical stability definitions are inapplicable and instead our new framework is required.

Item Type:
Journal Article
Journal or Publication Title:
Chaos
Subjects:
ID Code:
165180
Deposited By:
Deposited On:
28 Jan 2022 10:52
Refereed?:
Yes
Published?:
Published
Last Modified:
04 May 2022 02:40