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Stabilization of cyclic processes by slowly varying forcing

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Article number123129
<mark>Journal publication date</mark>30/12/2021
Issue number12
Number of pages34
Publication StatusPublished
<mark>Original language</mark>English


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.