A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks

作者：Rao Shodhan^*; van der Schaft Arjan; Jayawardhana Bayu

来源：Journal of Mathematical Chemistry, 2013, 51(9): 2401-2422.

DOI：10.1007/s10910-013-0218-8

• Weighted Laplacian matrix
• Linkage classes
• Zero-deficiency networks
• Persistence conjecture
• Equilibria
• Schur complement

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.

• 出版日期2013-10