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.
Original language | English |
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Journal | Chaos: an interdisciplinary journal of nonlinear science |
Volume | 31 |
Issue number | 12 |
DOIs | |
Publication status | Published - Dec 2021 |
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New mathematical framework pioneers a theory of stability of interacting systems
8/04/22
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