Discontinuous Spirals of Stable Periodic Oscillations

Achim Sack, Joana G. Freire, Erik Lindberg, Thorsten Pöschel, Jason A. C. Gallas

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Abstract

We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase orderly without bound.
Such complex patterns emerge forming self-similar discontinuous phases that combine in an artful way to produce large discontinuous spirals of stability. This unanticipated discrete accumulation of stability phases was detected experimentally and numerically in a Duffing-like proxy specially designed to bypass noisy
spectra conspicuously present in driven oscillators. Discontinuous spirals organize the dynamics over extended parameter intervals around a focal point. They are useful to optimize locking into desired oscillatory modes and to control complex systems. The organization of oscillations into discontinuous
spirals is expected to be generic for a class of nonlinear oscillators.
Original languageEnglish
JournalScientific Reports
Volume3
Pages (from-to)3350
Number of pages7
ISSN2045-2322
DOIs
Publication statusPublished - 2013

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