On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics

van der Schaft, A., Rao, S. & Jayawardhana, B., 2013, In : Siam Journal on Applied Mathematics. 73, 2, p. 953-973 21 p.

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Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the same time the structure of the complex graph and the stoichiometry of the network, and which admits a direct thermodynamical interpretation. This formulation allows us to easily characterize the set of positive equilibria and their stability properties. Furthermore, we develop a framework for interconnection of chemical reaction networks, and we discuss how the formulation leads to a new approach for model reduction.
Original languageEnglish
Pages (from-to)953-973
Number of pages21
JournalSiam Journal on Applied Mathematics
Issue number2
Publication statusPublished - 2013


  • model reduction, interconnection, equilibria, weighted Laplacian matrix, complex graph, mass action kinetics, chemical reaction networks

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