title: Discontinuous spirals of stable periodic oscillations.
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.
authors.affiliation: Institute for Multiscale Simulations, Friedrich-Alexander Universität, D-91052 Erlangen, Germany.
authors.forename: Achim
authors.initials: A
authors.lastname: Sack
authors.forename: Joana G
authors.initials: JG
authors.lastname: Freire
authors.forename: Erik
authors.initials: E
authors.lastname: Lindberg
authors.forename: Thorsten
authors.initials: T
authors.lastname: Pöschel
authors.forename: Jason A C
authors.initials: JA
authors.lastname: Gallas