ON THE MATHEMATICAL STRUCTURE OF BALANCED CHEMICAL REACTION NETWORKS GOVERNED BY MASS ACTION KINETICS
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 sa...
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| Published in | SIAM journal on applied mathematics Vol. 73; no. 2; pp. 953 - 973 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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| Subjects | |
| Online Access | Get full text |
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| 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. |
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| AbstractList | 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. [PUBLICATION 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 RAO, SHODHAN JAYAWARDHANA, BAYU |
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| Cites_doi | 10.1016/j.mbs.2007.07.003 10.1017/S0033583500000081 10.1016/j.sysconle.2010.05.005 10.1137/S0036139904440278 10.1007/BF00251225 10.1109/TCS.1974.1083946 10.1515/zpch-1902-3919 10.1016/0009-2509(87)80099-4 10.1074/jbc.274.42.30169 10.1137/090779401 10.1016/S0009-2509(99)00028-7 10.1007/BF00281751 10.1109/9.935056 10.1137/11082631X 10.1007/BF00375614 10.3166/ejc.15.398-406 10.1016/j.automatica.2011.03.010 10.1016/0009-2509(89)85124-3 10.1007/BF00255664 |
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| Title | ON THE MATHEMATICAL STRUCTURE OF BALANCED CHEMICAL REACTION NETWORKS GOVERNED BY MASS ACTION KINETICS |
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