Model Reduction for Reaction-Diffusion Systems: Bifurcations in Slow Invariant Manifolds

Abstract

Slow invariant manifolds (SIM) are calculated for spatially inhomogeneous closed reactive systems to obtain a model reduction. A simple oxygen dissociation reaction-diffusion system is evaluated. SIMs are calculated using a robust method of finding the system's equilibria and integrating to find heteroclinic orbits. Diffusion effects are obtained by using a Galerkin method to project the infinite dimensional dynamical system onto a low dimensional approximate inertial manifold. This projection rigorously accounts for the coupling of reaction and diffusion processes. An analytic coupling between reaction and diffusion time scales is shown to be a function of length scale. A critical length scale is identified where reaction and diffusion time scales are equal. At this critical length scale, a supercritical pitchfork bifurcation occurs which changes the SIM.