  This article is concerned with the stability and long-time dynamics of
structures arising from a structureless state. The paradigm is suggested by
developmental biology, where morphogenesis is thought to result from a
competition between chemical reactions and spatial diffusion. A system of two
reaction-diffusion equations for the concentrations of two morphogens is
reduced to a finite system of ordinary differential equations. The stability of
bifurcated solutions of this system is analyzed, and the long-time asymptotic
behavior of the bifurcated solutions is established rigorously. The
Schnakenberg and Gierer-Meinhardt equations are discussed as examples.
