DYNAMICS OF SELF-REPLICATING PATTERNS IN REACTION-DIFFUSION SYSTEMS

Recently solutions to a simple reaction diffusion system have been dis covered in which localized structures (spots) make copies of themselve s. In this Letter we analyze the one-dimensional analog of this proces s in which replication occurs until the domain is filled with a period ic array of spots. We provide a heuristic explanation of why this repl ication process should occur in a broad class of systems. Time depende nt solutions are developed for model systems and their analytic struct ures investigated.