Resonant and nonresonant patterns in forced oscillators

Abstract

Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.