ANALYSIS OF BIFURCATIONS IN REACTION-DIFFUSION SYSTEMS WITH NO-FLUX BOUNDARY-CONDITIONS - THE SELKOV MODEL

A plot of the bifurcation diagram for a two-component reaction-diffusi on equation with no-flux boundary conditions reveals an intricate web of competing stable and unstable states. By studying the one-dimension al Sel'kov model, we show how a mixture of local, global and numerical analysis can make sense of several aspects of this complex picture. T he local bifurcation analysis, via the power of singularity theory, gi ves us a framework to work in. We can then fill in the details with nu merical calculations, with the global analytic results fixing the outl ine of the solution set. Throughout, we discuss to what extent our res ults can be applied to other models.