Oscillatory clusters in a model of the photosensitive Belousov-Zhabotinskyreaction system with global feedback

Oscillatory cluster patterns are studied numerically in a reaction-diffusio n model of the photosensitive Belousov-Zhabotinsky reaction supplemented wi th a global negative feedback. In one- and two-dimensional systems. familie s of cluster patterns arise for intermediate values of the feedback strengt h. These patterns consist of spatial domains of phase-shifted oscillations. The phase of the oscillations is nearly constant for all points within a d omain. Two-phase clusters display antiphase oscillations: three-phase clust ers 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 f or two-phase clusters become stationary after a transient period, while bor ders drift in the case of three-phase clusters. We study the evolving borde r 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-ph ase clusters results in formation of spiral clusters-a combination of a fas t oscillating cluster with a slow spiraling movement of the domain border. At higher feedback coefficient, irregular cluster patterns arise, consistin g of domains that change their shape and position in an irregular manner. L ocalized irregular and regular clusters arise for parameters close to the b oundary between the oscillatory region and the reduced steady state region of the phase space.