Bistability and oscillations in chemical reaction networks

DOI10.1007/s00285-008-0234-7zbMath1311.92088OpenAlexW1977161816WikidataQ46235085 ScholiaQ46235085MaRDI QIDQ843313

Mirela Domijan, Markus Kirkilionis

Publication date: 12 October 2009

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-008-0234-7

zbMATH Keywords

bifurcationsbistabilitystoichiometric network analysispositive equilibria

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Bifurcations of singular points in dynamical systems (37G10)

Related Items (21)

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Uses Software

• CoCoA
• Macaulay2
• Magma
• Mathematica
• SINGULAR
• modst.lib
• toric.lib

Cites Work

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• Graph theory and qualitative analysis of reaction networks
• Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models
• A theorem on refining division orders by the reverse lexicographic order
• Elements of applied bifurcation theory.
• Criterion of Hopf bifurcations without using eigenvalues
• The Magma algebra system. I: The user language
• Modular algorithms for computing Gröbner bases.
• Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems
• Understanding bistability in complex enzyme-driven reaction networks
• SINGULAR
• The Mathematica GuideBook for Symbolics
• Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property

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