Chemical waves in a two-dimensional oscillating system

The early stages of the spontaneous desynchronization of chemical oscillations of the limit cycle type in a two-dimensional medium are investigated. It is shown in the framework of a reaction-diffusion kinetics that the behavior of the system is governed by the phase dynamics. Target patterns are radiated from centers which are spontaneously emitted by the system. They have various characteristic frequencies which are always larger than the frequency of the bulk oscillations. The statistical distribution of these centers is shown to depend on the wavelength of the corresponding waves and on the parameters of the limit cycle. Rotating spiral waves which correspond to vortexlike phase fluctuations have a vanishingly small probability and have to be initiated.