Structure of solution manifolds in a strongly coupled elliptic system

In this paper we study the steady-state solutions of a reaction-diffusionmodel, the Selkov scheme for glycolysis, under homogeneous Dirichletboundary conditions. Near to thermodynamic equilibrium, thestructure and stability of solutions are fully described. Abifurcation analysis is carried out, using the size of the regionin which the reaction takes place and one diffusion coefficientas main bifurcation parameters. The analysis helps us to understandthe nature of the bifurcation points, and determines the shapesand stability of the bifurcating manifolds in the neighbourhoodof the constant state. Local convergence of spectral methodsis shown, and some global pictures are calculated using path-followingtechniques. The framework we use can be applied to a wide varietyof reaction-diffusion systems. ^*Permanent address: Dpto. de Matemtica Aplicada, Fac. de CenciasQumicas, Universidad Complutense, 28040-Madrid, Spain. Current address: Department of Mathematics, Paisley Collegeof Technology, High Street, Paisley, Renfrewshire PA1 2BE, UK. Permanent address: Dpto. de Matemtica, Fac. de Matemtca, Astronomiay Fisica, Universidad National de Crdoba, 5000-Crdoba, R.Argentina.