Fast-slow vector fields of reaction-diffusion systems

A geometrically invariant concept of fast-slow vector fields perturbed by transport terms describing molecular diffusion is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields for ODEs to reaction-diffusion systems with chemical reactions having wide range of characteristic time scales, while transport processes remain comparatively slow. Under this assumption we developed a decomposition into a fast and slow subsystems. It is assumed that the transport terms for the fast subsystem can be neglected to the leading order. For the slow subsystem we modify a concept of singularly perturbed profiles proposed in our previous works. The results are used to justify and to modify an algorithm of reaction-diffusion manifolds (REDIMs). The modified REDIM method is applied to the Michaelis-Menten model to illustrate the suggested approach.