Symmetry-breaking rhythms in coupled, identical fast-slow oscillators

Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, Theodore Vo

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Symmetry-breaking in coupled, identical, fast-slow systems produces a rich, dramatic variety of dynamical behavior - such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly. We find symmetry-breaking rhythms in which one oscillator exhibits small-amplitude oscillations, while the other exhibits phase-shifted small-amplitude oscillations, large-amplitude oscillations, mixed-mode oscillations, or even undergoes an explosion of limit cycle canards. Two prototypical fast-slow systems illustrate the method: the van der Pol equation that describes electrical circuits and the Lengyel-Epstein model of chemical oscillators.

Original languageEnglish
Article number011102
Number of pages15
Issue number1
Publication statusPublished - Jan 2023

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