Static reaction–diffusion structures in folded slow manifold systems

Abstract

Static dissipative structures are obtained analytically for multiple time scale systems with folded slow manifolds. We find that the associated free boundary problem displays much of the richness of the full reaction–diffusion system. For a simple one-dimensional structure the pattern is shown to be linearly stable. Spoke patterns in a disk are calculated exactly. Since one type of static pattern in a disk was shown earlier to unfold into a rotating wave, these patterns are also of interest as the basis for the analysis of a class of multiple arm rotors. In a second special limiting case the patterns are shown to be in the form of narrow ‘‘double layers’’ in two-dimensional systems. Double layer patterns in a disk are obtained.