A Graph-theoretic Framework for Model Reduction Using Time-scale Analysis of Complex Reaction Networks

The orders of magnitude variation in rates typical in formulating a kinetic model for a complex reaction network, results in time scale separation that makes the system inherently stiff for simulation. In this work, a graph-theoretic framework is developed for the time scale decomposition of reaction systems into slow and fast time scales; the pseudo-species that evolve only in the slow time scale are identified. The reaction network is represented using a directed bi-partite graph and closed walks are used to identify interactions between species participating in the fast/equilibrated reactions. Subsequently, an algorithm which connects the closed walks to form the pseudo-species is utilized to eliminate the fast reaction rate terms. Two example reaction systems are considered to show the efficacy of the framework.