A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks

DOI10.1007/s10910-013-0218-8zbMath1285.05169arXiv1211.6643OpenAlexW2033198230MaRDI QIDQ2443860

Shodhan Rao, Bayu Jayawardhana, Arjan J. Van der Schaft

Publication date: 8 April 2014

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

Full work available at URL: https://arxiv.org/abs/1211.6643

zbMATH Keywords

Schur complementequilibriaweighted Laplacian matrixlinkage classespersistence conjecturezero-deficiency networks

Mathematics Subject Classification ID

Applications of graph theory (05C90) Deterministic network models in operations research (90B10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Stability of solutions to ordinary differential equations (34D20) Asymptotic properties of solutions to ordinary differential equations (34D05) Control/observation systems governed by ordinary differential equations (93C15) Large-scale systems (93A15)

Related Items (23)

Core-Periphery Detection in Hypergraphs ⋮ Structure-Preserving Model Reduction of Physical Network Systems ⋮ Model Reduction of Biochemical Reactions Networks by Tropical Analysis Methods ⋮ Interpreting nucleation as a network formation process ⋮ Stability analysis of the Michaelis-Menten approximation of a mixed mechanism of a phosphorylation system ⋮ Port-Hamiltonian modeling of non-isothermal chemical reaction networks ⋮ Handling Biological Complexity Using Kron Reduction ⋮ Realizations of quasi-polynomial systems and application for stability analysis ⋮ Structural analysis in biology: a control-theoretic approach ⋮ Physical network systems and model reduction ⋮ Computing zero deficiency realizations of kinetic systems ⋮ Reduction of Chemical Reaction Networks with Approximate Conservation Laws ⋮ Qualitative analysis of an ODE model of a class of enzymatic reactions. Some results on global stability of messenger RNA-microRNA interaction ⋮ Complex Balancing Reconstructed to the Asymptotic Stability of Mass-Action Chemical Reaction Networks with Conservation Laws ⋮ Balanced truncation of networked linear passive systems ⋮ Complex and detailed balancing of chemical reaction networks revisited ⋮ Modeling of physical network systems ⋮ Unnamed Item ⋮ A network dynamics approach to chemical reaction networks ⋮ A Graphic Formulation of Nonisothermal Chemical Reaction Systems and the Analysis of Detailed Balanced Networks ⋮ Diffusion and consensus on weakly connected directed graphs ⋮ Lyapunov Function Partial Differential Equations for Chemical Reaction Networks: Some Special Cases ⋮ 11 Reduced-order modeling of large-scale network systems

Cites Work

• Unnamed Item
• A tutorial on chemical reaction network dynamics
• How far is complex balancing from detailed balancing?
• Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates
• Characterization and partial synthesis of the behavior of resistive circuits at their terminals
• Toric dynamical systems
• Guaranteed error bounds for structured complexity reduction of biochemical networks
• The existence and uniqueness of steady states for a class of chemical reaction networks
• On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics
• Persistence Results for Chemical Reaction Networks with Time-Dependent Kinetics and No Global Conservation Laws
• A Proof of the Global Attractor Conjecture in the Single Linkage Class Case
• Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction
• Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property
• Global stability of complex balanced mechanisms

This page was built for publication: A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks