A network dynamics approach to chemical reaction networks

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a...
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Autor*in:	van der Schaft, A. J [verfasserIn] Rao, S Jayawardhana, B

Format:	Artikel
Sprache:	Englisch

Erschienen:	2016

Rechteinformationen:	Nutzungsrecht: © 2015 Taylor & Francis 2015 © info:eu-repo/semantics/closedAccess

Schlagwörter:	chemical reaction networks consensus dynamics Network dynamics network dynamics To be checked by Faculty nonlinear systems Chemical reactions

Übergeordnetes Werk:	Enthalten in: International journal of control - London : Taylor & Francis, 1965, 89(2016), 4, Seite 731-745
Übergeordnetes Werk:	volume:89 ; year:2016 ; number:4 ; pages:731-745

Links:	Volltext Link aufrufen Link aufrufen

DOI / URN:	10.1080/00207179.2015.1095353

Katalog-ID:	OLC1974535703

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topic_title	620 DNB A network dynamics approach to chemical reaction networks chemical reaction networks consensus dynamics Network dynamics network dynamics To be checked by Faculty nonlinear systems Chemical reactions
topic	ddc 620 misc chemical reaction networks misc consensus dynamics misc Network dynamics misc network dynamics misc To be checked by Faculty misc nonlinear systems misc Chemical reactions
topic_unstemmed	ddc 620 misc chemical reaction networks misc consensus dynamics misc Network dynamics misc network dynamics misc To be checked by Faculty misc nonlinear systems misc Chemical reactions
topic_browse	ddc 620 misc chemical reaction networks misc consensus dynamics misc Network dynamics misc network dynamics misc To be checked by Faculty misc nonlinear systems misc Chemical reactions
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title	A network dynamics approach to chemical reaction networks
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title_full	A network dynamics approach to chemical reaction networks
author_sort	van der Schaft, A. J
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title_sort	network dynamics approach to chemical reaction networks
title_auth	A network dynamics approach to chemical reaction networks
abstract	A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.
abstractGer	A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.
abstract_unstemmed	A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.
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title_short	A network dynamics approach to chemical reaction networks
url	http://dx.doi.org/10.1080/00207179.2015.1095353 http://www.tandfonline.com/doi/abs/10.1080/00207179.2015.1095353 http://www.narcis.nl/publication/RecordID/oai:pure.rug.nl:publications%2Fe9818e94-01fd-4c33-87b7-0cc8456daba7
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up_date	2024-07-04T04:31:23.559Z
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