A Singular Perturbation Analysis for a Reaction‐Diffusion System Describing Pattern Formation

A reaction‐diffusion system describing a simple activator‐inhibitor reaction is investigated in the limiting case of “very large” diffusion rate of the inhibitor. Using singular perturbation techniques, an inner and an outer expansion are derived. The latter, describing the large‐time behavior of the system, is governed by equations that, in the first orders of approximation, possess asymptotically stable space‐inhomogeneous equilibria (patterns), and whose set of equilibria is globally attractive.