Sack, Achim4; Freire, Joana G.4; Lindberg, Erik2; Pöschel, Thorsten4; Gallas, Jason A. C.4
1 Department of Electrical Engineering, Technical University of Denmark2 Department of Information Technology, Technical University of Denmark3 Electronics, Department of Electrical Engineering, Technical University of Denmark4 Friedrich-Alexander Universität
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.