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arXiv · 1211.6643

A Graph-Theoretical Approach for the Analysis and Model Reduction of Complex-Balanced Chemical Reaction Networks

Shodhan Rao·Arjan van der Schaft·Bayu Jayawardhana
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Abstract

In this paper we derive a compact mathematical formulation describing the dynamics of chemical reaction networks that are complex-balanced and are governed by mass action kinetics. The formulation is based on the graph of (substrate and product) complexes and the stoichiometric information of these complexes, and crucially uses a balanced weighted Laplacian matrix. It is shown that this formulation leads to elegant methods for characterizing the space of all equilibria for complex-balanced networks and for deriving stability properties of such networks. We propose a method for model reduction of complex-balanced networks, which is similar to the Kron reduction method for electrical networks and involves the computation of Schur complements of the balanced weighted Laplacian matrix.

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Shodhan Rao, Arjan van der Schaft, Bayu Jayawardhana. 2012-11-28. A Graph-Theoretical Approach for the Analysis and Model Reduction of Complex-Balanced Chemical Reaction Networks. https://arxiv.org/abs/1211.6643

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