Invariant Grids: Method of Complexity Reduction in Reaction Networks

Abstract

Complexity in the description of big chemical reaction networks has both structural (number of species and reactions) and temporal (very different reaction rates) aspects. A consistent way to make model reduction is to construct the invariant manifold which describes the asymptotic system behaviour. In this paper we present a discrete analog of this object: an invariant grid. The invariant grid is introduced independently from the invariant manifold notion and can serve to represent the dynamic system behaviour as well as to approximate the invariant manifold after refinement. The method is designed for pure dissipative systems and widely uses their thermodynamic properties but allows also generalizations for some classes of open systems. The method is illustrated by two examples: the simplest catalytic reaction (Michaelis-Menten mechanism) and the hydrogen oxidation.