Pattern formation in a coupled cubic autocatalator system

The spatiotemporal structures that can arise in two identicalcells, each governed by cubic autocatalator kinetics and coupledvia the diffusive interchange of the autocatalyst, are discussed.The equations obtained by linearizing about the spatially uniformsolution are considered first. These are seen to give the possibilityof bifurcations to spatially nonuniform solutions at both thesame parameter values as for the uncoupled system and, for relativelyweak coupling strengths ß, at further parameter valuesnot present in the uncoupled system. A weakly nonlinear analysisis then performed to describe the solution close to the bifurcationpoints and under the assumption of small ß. This givesfurther insights into the nature of the spatially nonuniformsolutions close to bifurcation, which are then followed numericallyusing a path-following technique. AU the extra solutions whichare due to the coupling are seen to be unstable close to theirbifurcation. However, these can undergo further secondary bifurcations,to produce new stable spatially nonuniform structures.