THE EFFECTS OF COUPLING ON PATTERN-FORMATION IN A SIMPLE AUTOCATALYTIC 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 a reactant, are discussed. The coupling gives rise to five spatially uniform steady states, one of which exists in !he u ncoupled system. By studying the linearized equations, it is found tha t three of these steady states, including that of the uncoupled system , may give rise to the possibility of bifurcations to spatially nonuni form steady states. In the case of the steady state corresponding to t hat of the uncoupled system, it is seen that the coupling leads to bif urcations not present in the uncoupled system which give rise to local ly stable nonuniform steady states. A weakly nonlinear analysis is dev eloped for both small and large coupling strength alpha, and for param eter values in a neighbourhood of the bifurcation points on the new st eady states. This clarifies the nature of the nonuniform solutions clo se to bifurcation, which are then followed numerically using a path-fo llowing technique. The coupling is found to produce extra nonuniform s teady solutions which are stable close to their bifurcation points.