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Patterns of spatial concentration profiles arising in one-dimensional reaction-diffusion systems in the course of variations of the characteristic dimension of the system (growth) are analyzed. The spatial profiles established and their changes depend on the character of the steady state pattern dependence on length. If the families of solutions (spatial profiles) arising at L = nL1*, nL2* form closed curves, and a slow (quasistationary) linear or exponential increase of the characteristic dimension is considered, then subsequently more complex patterns of spatial concentration profiles appear regularly in a reproducible way. The system keeps every established pattern for a fixed interval of time which depends on the rate of growth. Implications for two different interpretations of the morphogen gradient formation in the models of embryogenesis are discused.
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Marek et al. (1980) studied this question.
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