Oscillatory cluster patterns in a homogeneous chemical system with global feedback
                         Vanag VK, Yang LF, Dolnik M, Zhabotinsky AM, Epstein IR
                                             NATURE
                                    406 (6794): 389-391 JUL 27 2000
Abstract:
Oscillatory clusters are sets of domains in which nearly all elements in a given domain oscillate with the same amplitude and
phase(1-4). They play an important role in understanding coupled neuron systems(5-8). In the simplest case, a system consists of
two clusters that oscillate in antiphase and can each occupy multiple fixed spatial domains. Examples of cluster behaviour in
extended chemical systems are rare, but have been shown to resemble standing waves(9-13), except that they lack a
characteristic wavelength. Here we report the observation of so-called 'localized clusters'-periodic antiphase oscillations in one
part of the medium, while the remainder appears uniform-in the Belousov-Zhabotinsky reaction-diffusion system with
photochemical global feedback. We also observe standing clusters with fixed spatial domains that oscillate periodically in time and
occupy the entire medium, and irregular clusters with no periodicity in either space or time, with standing clusters transforming into
irregular clusters and then into localized clusters as the strength of the global negative feedback is gradually increased. By
incorporating the effects of global feedback into a model of the reaction, we are able to simulate successfully the experimental
data.