We present a novel approach to the dynamics of spatially discrete reaction-diffusion equations. The approach addresses systems with active regions on the submicrometer length scale arranged with distances of a few micrometer. The size of the active region is determined by the production of diffusing substance. The linear stability analysis reveals that due to spatial discreteness, diffusion becomes one of the major determinants of the stability of the reaction dynamics. We illustrate this new approach with Ca 2+ dynamics in living cells.
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