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Bradley Marts, Aric Hagberg, Ehud Meron and Anna L. Lin, "Resonant and non-resonant patterns in forced oscillators ", Chaos, vol. 16, pp. 037113, 2006

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(FHN) model and the complex Ginzburg-Landau (CGL) equation, with additional terms describing periodic forcing.

BibTeX Entry

@article{marts-2006-resonant,
author = {Bradley Marts and Aric Hagberg and Ehud Meron and Anna L. Lin},
title = {Resonant and non-resonant patterns in forced oscillators },
year = {2006},
urlpdf = {http://math.lanl.gov/~hagberg/Papers/marts-2006-resonant.pdf},
journal = {Chaos},
volume = {16},
pages = {037113}
}