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Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a simple two-variable reaction-diffusion system and find there is a spatio-temporally oscillating solution (STOS) in parameter regions where linear analysis predicts a pure Turing instability and no Hopf instability. We compute the boundary of the STOS and spatially non-uniform solution (SSNS) regions and investigate what features control its behavior.

Type

Conference paper

Publication Date

01/2007

Volume

50

Pages

234 - 238

Keywords

reaction-diffusion, skin, WAVE, oscillatory Turing pattern, nonlinear, SPATIOTEMPORAL DYNAMICS