The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems
Open accessAbstract
The dynamics of complex isothermal reactors are studied in general terms with special focus on connections between reaction network structure and the capacity of the corresponding differential equations to admit unstable behavior. As in some earlier work, the principal results rely on a classification of reaction networks by means of an easily computed non-negative integer index called the deficiency. This index often provides nontrivial information about the kind of dynamics that can be expected. Part of the previously reported Deficiency Zero Theorem is substantially generalized by the Deficiency One Theorem. The foundation is laid for a companion article containing a theory of multiple steady states generated by reaction networks of deficiency one.
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Citations
Cites
Thermodynamic Theory of Structure, Stability and Fluctuations
Glansdorff, P., Prigogine, I., & Hill, R. N. (1973) · American Journal of Physics · doi:10.1119/1.1987158 · Cited by 2,973
Mathematical Aspects of Reacting and Diffusing Systems
Fife, P. C. (1979) · Lecture notes in biomathematics · doi:10.1007/978-3-642-93111-6 · Cited by 1,283
Horn, F., & Jackson, R. (1972) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00251225 · Cited by 1,014
Complex balancing in general kinetic systems
Feinberg, M. (1972) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00255665 · Cited by 385
Self-citationNecessary and sufficient conditions for complex balancing in chemical kinetics
Horn, F. (1972) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00255664 · Cited by 352
Stability of Complex Reaction Networks
Clarke, B. L. (1980) · Advances in Chemical Physics · doi:10.1002/9780470142622.ch1 · Cited by 310
Feinberg, M. (1988) · Chemical Engineering Science · doi:10.1016/0009-2509(88)87122-7 · Cited by 212
Self-citationDynamics of open chemical systems and the algebraic structure of the underlying reaction network
Feinberg, M., & Horn, F. J. M. (1974) · Chemical Engineering Science · doi:10.1016/0009-2509(74)80195-8 · Cited by 171
Self-citationChemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces
Feinberg, M., & Horn, F. (1977) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00250853 · Cited by 133
Self-citationChemical Oscillations, Multiple Equilibria, and Reaction Network Structure
Feinberg, M. (1980) · Elsevier eBooks · doi:10.1016/b978-0-12-669550-2.50008-7 · Cited by 66
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Research works printed but not linked: 3
- Edelstein, 1970, A biochemical model with multiple steady states and hysteresis, J. Theor. Biol., 29, 57, 10.1016/0022-5193(70)90118-9 · doi:10.1016/0022-5193(70)90118-9
- Feinberg, 1986, The existence and uniqueness of steady states for some chemical reaction networks of positive deficiency, to appear, Arch. Rational Mech. Anal.
- Lyberatos, 1984, Steady-state multiplicity and bifurcation analysis via the Newton polyhedron approach, Chem. Engng Sci., 39, 947, 10.1016/0009-2509(84)87002-5 · doi:10.1016/0009-2509(84)87002-5
Cited by
Port-Hamiltonian Systems Theory: An Introductory Overview
van der Schaft, A., & Jeltsema, D. (2014) · Foundations and Trends® in Systems and Control · doi:10.1561/2600000002 · Cited by 638
Structural Sources of Robustness in Biochemical Reaction Networks
Shinar, G., & Feinberg, M. (2010) · Science · doi:10.1126/science.1183372 · Cited by 379
Self-citationDynamics of Cdc42 network embodies a Turing‐type mechanism of yeast cell polarity
Goryachev, A. B., & Pokhilko, A. V. (2008) · FEBS Letters · doi:10.1016/j.febslet.2008.03.029 · Cited by 327
Understanding bistability in complex enzyme-driven reaction networks
Craciun, G., Tang, Y., & Feinberg, M. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0602767103 · Cited by 300
Self-citationMultiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property
Craciun, G., & Feinberg, M. (2005) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139904440278 · Cited by 292
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Metadata
- Authors
- Feinberg, M.
- Venue
- Chemical Engineering Science
- Publisher
- Elsevier BV
- Published
- 1987
- Volume
- 42
- Issue
- 10
- Pages
- 2229-2268
- ISSN
- 0009-2509 (ISSN-L)
- OpenAlex
- W2094781369
- Cited by
- 744
- References
- 12
- FWCI
- 6.50
- Type
- journal article
- Language
- en
- Open access
- hybrid
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/legal/tdmrep-license (tdm)
- creativecommons.org/licenses/by-nc-nd/4.0/ (vor, 5756 d)
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- Feinberg, M. (1987). Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems. Chemical Engineering Science. https://doi.org/10.1016/0009-2509(87)80099-4
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
