PATTERN-FORMATION IN A COUPLED CUBIC AUTOCATALATOR SYSTEM

The spatiotemporal structures that can arise in two identical cells, e ach governed by cubic autocatalator kinetics and coupled via the diffu sive interchange of the autocatalyst, are discussed. The equations obt ained by linearizing about the spatially uniform solution are consider ed first. These are seen to give the possibility of bifurcations to sp atially nonuniform solutions at both the same parameter values as for the uncoupled system and, for relatively weak coupling strengths beta, at further parameter values not present in the uncoupled system. A we akly nonlinear analysis is then performed to describe the solution clo se to the bifurcation points and under the assumption of small beta. T his gives further insights into the nature of the spatially nonuniform solutions close to bifurcation, which are then followed numerically u sing a path-following technique. All the extra solutions which are due to the coupling are seen to be unstable close to their bifurcation. H owever, these can undergo further secondary bifurcations, to produce n ew stable spatially nonuniform structures.