Oscillatory cluster patterns in a homogeneous chemical system with global feedback

Oscillatory clusters are sets of domains in which nearly all elements in a given domain oscillate with the same amplitude and phase1,2,3,4. They play an important role in understanding coupled neuron systems5,6,7,8. 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 waves9,10,11,12,13, 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.