Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks

DOI10.1016/j.mbs.2012.05.007zbMath1319.92018OpenAlexW2010321157WikidataQ51354791 ScholiaQ51354791MaRDI QIDQ452456

Marc R. Roussel, Maya Mincheva

Publication date: 21 September 2012

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mbs.2012.05.007

zbMATH Keywords

pattern formationbiochemical reaction networksgraph-theoretic conditionsTuring-Hopf instability

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Systems biology, networks (92C42)

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Uses Software

• XPPAUT

Cites Work

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• Oscillations in biochemical reaction networks arising from pairs of subnetworks
• Oscillations in non-mass action kinetics models of biochemical reaction networks arising from pairs of subnetworks
• Modeling transcriptional control in gene networks -- methods, recent results, and future directions
• Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models
• Inertia characteristics of self-adjoint matrix polynomials
• Elements of applied bifurcation theory.
• Mathematical physiology
• Criterion of Hopf bifurcations without using eigenvalues
• Parallel concepts in graph theory
• Dynamical behaviour of biological regulatory networks. I: Biological role of feedback loops and practical use of the concept of the loop- characteristic state
• Pattern formation in systems with one spatially distributed species
• Some remarks on matrix stability with application to Turing instability
• Computing Hopf Bifurcations I
• Simulating, Analyzing, and Animating Dynamical Systems
• Matrices, Digraphs, and Determinants
• Bidiagonal Factorizations of Totally Nonnegative Matrices
• The chemical basis of morphogenesis
• Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property
• Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph
• On the Total Nonnegativity of the Hurwitz Matrix
• Diffusion-driven instability in reaction-diffusion systems
• A simple method of parameter space determination for diffusion-driven instability with three species
• Turing instabilities in general systems