Singularly perturbed monotone systems and an Application to double phosphorylation cycles

DOI10.1007/s00332-008-9021-2zbMath1176.34043arXivmath/0701575OpenAlexW3103597052MaRDI QIDQ1015419

Liming Wang, Eduardo D. Sontag

Publication date: 8 May 2009

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701575

Mathematics Subject Classification ID

Singular perturbations of ordinary differential equations (34D15) Cell biology (92C37) Asymptotic properties of solutions to ordinary differential equations (34D05) Singular perturbations for ordinary differential equations (34E15) Monotone systems involving ordinary differential equations (34C12) Monotone flows as dynamical systems (37C65)

Related Items (9)

Analysis of a Reduced Model of Epithelial–Mesenchymal Fate Determination in Cancer Metastasis as a Singularly-Perturbed Monotone System ⋮ Stability analysis of the Michaelis-Menten approximation of a mixed mechanism of a phosphorylation system ⋮ Unnamed Item ⋮ Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2 ⋮ A proof of bistability for the dual futile cycle ⋮ Structural properties of the MAPK pathway topologies in PC12 cells ⋮ Precluding oscillations in Michaelis-Menten approximations of dual-site phosphorylation systems ⋮ Reduction and stability analysis of a transcription-translation model of RNA polymerase ⋮ A symbolic computation approach to a problem involving multivariate Poisson distributions

Cites Work

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• On the number of steady states in a multiple futile cycle
• Geometric singular perturbation theory for ordinary differential equations
• Mathematical biology. Vol. 1: An introduction.
• Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles
• Molecular systems biology and control
• Stability and convergence in strongly monotone dynamical systems.
• Differential equations and convergence almost everywhere in strongly monotone semiflows
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Some remarks on a boundedness assumption for monotone dynamical systems
• On the Global Stability of Cooperative Systems
• A unified framework for input-to-state stability in systems with two time scales
• Asymptotic Tracking for Constrained Monotone Systems
• Singular perturbations and input-to-state stability
• Invariant manifolds in singular perturbation problems for ordinary differential equations

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