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First-order chemical reaction networks I: theoretical considerations

Authors
  • Tóbiás, Roland1
  • Stacho, László L.2
  • Tasi, Gyula1
  • 1 University of Szeged, Department of Applied and Environmental Chemistry, Rerrich B. tér 1, Szeged, 6720, Hungary , Szeged (Hungary)
  • 2 University of Szeged, Bolyai Institute, Aradi Vértanúk tere 1, Szeged, 6720, Hungary , Szeged (Hungary)
Type
Published Article
Journal
Journal of Mathematical Chemistry
Publisher
Springer International Publishing
Publication Date
Jun 14, 2016
Volume
54
Issue
9
Pages
1863–1878
Identifiers
DOI: 10.1007/s10910-016-0655-2
Source
Springer Nature
Keywords
License
Yellow

Abstract

Our former study Tóbiás and Tasi (J Math Chem 54:85, 2016) is continued, where a simple algebraic solution was given to the kinetic problem of triangle, quadrangle and pentangle reactions. In the present work, after defining chemical reaction networks and their connectedness, first-order chemical reaction networks (FCRNs) are studied on the basis of the results achieved by Chellaboina et al. (Control Syst 29:60, 2009). First, it is proved that an FCRN is disconnected iff its coefficient matrix is block diagonalizable. Furthermore, mass incompatibility is used to interpret the reducibility of subconservative networks. For conservative FCRNs, the so-called marker network is introduced, which is linearly conjugate to the original one, to describe the zero eigenvalue associated to the coefficient matrix of an FCRN. Instead of using graph-theoretical concepts, simple algebraic tools are applied to present and solve these problems. As an illustration, an industrially important ten-component (formal) FCRN is presented which has algebraically exact solution.

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