Finding all steady state solutions of chemical kinetic models

DOI10.1016/j.nonrwa.2004.02.002zbMath1089.80004OpenAlexW1965889434MaRDI QIDQ2572160

John J. Tyson, Layne T. Watson, Jason W. Zwolak

Publication date: 14 November 2005

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2004.02.002

zbMATH Keywords

Steady statePolynomial systemHomotopyBiological modelChemical kinetic model

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Stability of solutions to ordinary differential equations (34D20) Chemical kinetics in thermodynamics and heat transfer (80A30) Numerical algorithms for specific classes of architectures (65Y10)

Related Items (5)

Shaping pulses to control bistable systems: analysis, computation and counterexamples ⋮ A mathematical model of the photosynthetic carbon metabolism has multiple steady states under the same parameter conditions ⋮ Mathematical analysis of the Tyson model of the regulation of the cell division cycle ⋮ A simple model of the Calvin cycle has only one physiologically feasible steady state under the same external conditions ⋮ KINSOLVER: A simulator for computing large ensembles of biochemical and gene regulatory networks

Uses Software

• HOMPACK90
• POLSYS_PLP
• XPPAUT

Cites Work

• A methodology for solving chemical equilibrium systems
• Algorithm 652
• Simulating, Analyzing, and Animating Dynamical Systems
• A globally convergent parallel algorithm for zeros of polynomial systems
• Algorithm 777: HOMPACK90
• Algorithm 801: POLSYS_PLP
• A Product-Decomposition Bound for Bezout Numbers

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