  This article describes a reduction of a nonautonomous Brusselator
reaction-diffusion system of partial differential equations on a spherical cap
with time dependent curvature using the method of centre manifold reduction.
Parameter values are chosen such that the change in curvature would cross
critical values which would change the stability of the patternless solution in
the constant domain case. The evolving domain functions and quasi-patternless
solutions are derived as well as a method to obtain this nonautonomous normal
form. The coefficients of such a normal form are computed and the reduction
solutions are compared to numerical solutions.
