On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics
- Author
- Arjan van der Schaft, Shodhan Rao (UGent) and Bayu Jayawardhana
- Organization
- Abstract
- 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.
- Keywords
- weighted Laplacian matrix, equilibria, complex graph, mass action kinetics, chemical reaction networks, interconnection, model reduction, STABILITY, RECEPTOR, SUFFICIENT CONDITIONS, PERSISTENCE, SYSTEMS, MODEL
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-6990067
- MLA
- van der Schaft, Arjan, et al. “On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics.” SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 73, no. 2, 2013, pp. 953–73, doi:10.1137/11085431X.
- APA
- van der Schaft, A., Rao, S., & Jayawardhana, B. (2013). On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics. SIAM JOURNAL ON APPLIED MATHEMATICS, 73(2), 953–973. https://doi.org/10.1137/11085431X
- Chicago author-date
- Schaft, Arjan van der, Shodhan Rao, and Bayu Jayawardhana. 2013. “On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics.” SIAM JOURNAL ON APPLIED MATHEMATICS 73 (2): 953–73. https://doi.org/10.1137/11085431X.
- Chicago author-date (all authors)
- van der Schaft, Arjan, Shodhan Rao, and Bayu Jayawardhana. 2013. “On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics.” SIAM JOURNAL ON APPLIED MATHEMATICS 73 (2): 953–973. doi:10.1137/11085431X.
- Vancouver
- 1.van der Schaft A, Rao S, Jayawardhana B. On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics. SIAM JOURNAL ON APPLIED MATHEMATICS. 2013;73(2):953–73.
- IEEE
- [1]A. van der Schaft, S. Rao, and B. Jayawardhana, “On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics,” SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 73, no. 2, pp. 953–973, 2013.
@article{6990067,
abstract = {{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.}},
author = {{van der Schaft, Arjan and Rao, Shodhan and Jayawardhana, Bayu}},
issn = {{0036-1399}},
journal = {{SIAM JOURNAL ON APPLIED MATHEMATICS}},
keywords = {{weighted Laplacian matrix,equilibria,complex graph,mass action kinetics,chemical reaction networks,interconnection,model reduction,STABILITY,RECEPTOR,SUFFICIENT CONDITIONS,PERSISTENCE,SYSTEMS,MODEL}},
language = {{eng}},
number = {{2}},
pages = {{953--973}},
title = {{On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics}},
url = {{http://doi.org/10.1137/11085431X}},
volume = {{73}},
year = {{2013}},
}
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