Oscillatory clusters in a model of the photosensitive Belousov-Zhabotinsky reaction system with global feedback
                              Yang LF, Dolnik M, Zhabotinsky AM, Epstein IR
                                       PHYSICAL REVIEW E
                                  62 (5): 6414-6420, Part A NOV 2000
Abstract:
Oscillatory cluster patterns are studied numerically in a reaction-diffusion model of the photosensitive Belousov-Zhabotinsky
reaction supplemented with a global negative feedback. In one- and two-dimensional systems. families of cluster patterns arise for
intermediate values of the feedback strength. These patterns consist of spatial domains of phase-shifted oscillations. The phase of
the oscillations is nearly constant for all points within a domain. Two-phase clusters display antiphase oscillations: three-phase
clusters contain three sets of domains with a phase shift equal to one-third of the period of the local oscillation. Border (nodal)
lines between domains for two-phase clusters become stationary after a transient period, while borders drift in the case of
three-phase clusters. We study the evolving border movement of the clusters, which, in most cases, leads to phase balance, i.e.,
equal areas of the different phase domains. Border curling of three-phase clusters results in formation of spiral clusters-a
combination of a fast oscillating cluster with a slow spiraling movement of the domain border. At higher feedback coefficient,
irregular cluster patterns arise, consisting of domains that change their shape and position in an irregular manner. Localized
irregular and regular clusters arise for parameters close to the boundary between the oscillatory region and the reduced steady
state region of the phase space.