Spatial structures in a reaction-diffusion system--detailed analysis of the "Brusselator"

Continuous dependence of spatially nonuniform concentration profiles for the 'Brussellator" reaction mechanims on the characteristic length of the system is given both for zero flux and fixed boundary conditions. Branches of solutions arising through primary bifurcation form closed curves. Secondary bifurcations giving rise to spatially asymmetric solutions exist for fixed boundary conditions. Results of a stability analysis of individual solutions are discussed. A method of composing complex spatial profiles for higher lengths from elementary solutions for smaller lenghts is suggested and tested in the case of zero flux boundary conditions. Emergence of subsequently more complex stable patterns in dependence on increasing length of the system suggests many similarities to gradual build up of complex morphogenetic patterns.