Diffusive Stability of Spatially Periodic Solutions of the Brusselator Model.

Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the canonical second-order system of reaction-diffusion equations given by the Brusselator model. Our results confirm that stability is accurately predicted in the small-amplitude limit by the formal Ginzburg-Landau amplitude equations, rigorously validating the standard weakly unstable approximation and the Eckhaus criterion. [ABSTRACT FROM AUTHOR]