Analysis of metabolic systems with complex slow and fast dynamics

DOI10.1007/BF02458446zbMath0678.92004OpenAlexW4250297611WikidataQ38608312 ScholiaQ38608312MaRDI QIDQ1124547

Ivan Dvořák, J.Šiška

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf02458446

zbMATH Keywords

limit cycleattractorbiochemistrytime hierarchyTikhonov's theoremenzymatic reactiongenetically driven enzyme turnoverproduct activation

Mathematics Subject Classification ID

Biochemistry, molecular biology (92C40) Averaging method for ordinary differential equations (34C29) Singular perturbations of ordinary differential equations (34D15) Chemical kinetics in thermodynamics and heat transfer (80A30)

Related Items (5)

Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics ⋮ New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis-Menten paper ⋮ Uniform Asymptotic Expansions beyond the tQSSA for the Goldbeter--Koshland Switch ⋮ Targeted reduction of complex models with time scale hierarchy -- a case study ⋮ A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

Cites Work

• Differential equations and their applications. An introduction to applied mathematics. 3rd ed
• Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks
• The ergodic theory of axiom A flows
• Conditions for the application of the steady-state approximation to systems of differential equations
• Bifurcation and catastrophe theory
• Differential Topology
• Differentiable dynamical systems
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