Mathematical analysis of an activation-inhibition system in a discrete field
The activation-inhibition model of \textit{H. Meinhardt} and \textit{A. Gierer} [see J. Theor. Biol. 85, 429-450 (1980)] is investigated in the particular case of a stringlike set of cells. This reaction-diffusion system is considered, from a topical point of view, as a nonautonomous dynamic system which rules the behavior of each cell. It was shown that, when no diffusion occurs, this system can have either no or one or two stable steady states. The effect of intercellular exchanges on the existence and stability of these steady states is studied, so as to apply this model to the investigation of the branching of a filamentous lower plant.
scientific article; zbMATH DE number 3883983