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Activators and Inhibitors in Pattern Formation
Author(s) -
Keener James P.
Publication year - 1978
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19785911
Subject(s) - activator (genetics) , reaction–diffusion system , amplitude , mathematics , chemistry , physics , mechanics , classical mechanics , mathematical analysis , biochemistry , receptor , optics
A wide class of diffusion reaction equations with activator‐inhibitor reaction dynamics are studied analytically. It is shown that when the inhibitor diffuses much faster than the activator, patterns with large amplitude nonuniformities may exist. It is further shown that with a slightly nonuniform source of activator, the patterns which emerge from the time dependent process have a directional preference. The results given coincide with the numerical results of Gierer and Meinhardt [6].