Recently solutions to a simple reaction diffusion system have been discovered in which localized structures (spots) make copies of themselves. In this Letter we analyze the one-dimensional analog of this process in which replication occurs until the domain is filled with a periodic array of spots. We provide a heuristic explanation of why this replication process should occur in a broad class of systems. Time dependent solutions are developed for model systems and their analytic structures investigated.
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Reynolds et al. (1994) studied this question.
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