Spatial organization of chemical oscillators via an averaging operator

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Abstract
Spatial interaction of chemical oscillators is usually described in terms of diffusion. In this paper an alternative model is considered which is described by the following equations: dX/dt=G (X,F[Y]), dY/dt=H (X,F[Y]), where F[Y] is an averaging operator of the values of Y (r,t) over a finite region. It is shown that in this case solutions corresponding to circular, spiral, and other waves are obtained. Thus simulation of phenomena observed in the Zhabotinsky reaction, fungi cultures, and circadian rhythms is obtained.

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