Model reduction by extended quasi-steady-state approximation

Journal of Mathematical Biology

Volumn 40, Issue 5, 2000, Pages 443-450

  Schneider, Klaus R ^a   Wilhelm, Thomas ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b LEIBNIZ INSTITUTE OF FRESHWATER ECOLOGY AND INLAND FISHERIES   (Germany)

Author keywords

Quasi steady state approximation; Singularly perturbed systems; Trimolecular autocatalator

Indexed keywords

ENZYME;

ARTICLE; BIOLOGICAL MODEL; KINETICS; METABOLISM;

ENZYMES; KINETICS; MODELS, BIOLOGICAL;

EID: 0034180406     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000026     Document Type: Article

References (24)

1. Alhumaizi, K., Aris, R.: Surveying a Dynamical System: A Study of the Gray-Scott Reaction in a Two-Phase Reactor, Pitman Research Notes in Mathematics, 341, Essex: Longman 1995
2. Bogoliubov, N.N., Mitropolskii, Yu. A.: Asymptotic methods in the theory of nonlinear oscillations, Hindustan Publ. Corp., 1961
3. Borghans, J.A.M., de Boer, R.J., Segel, L.A.: Extending the quasi-steady-state approximation by changing variables, Bull. Math. Biol., 58, 43-63 (1996)
4. Chen, L. Y., Goldenfeld, N., Oono, Y.: Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett., 73, 1311-1315 (1994)
5. Cook, G.B., Gray, P., Knapp, D.G., Scott, S.K.: Bimolecular Routes to Cubic Autocatalysis, J. Phys. Chem., 93, 2749-2755 (1989)
6. Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions, Manchester 1989
7. Fenichel, N.: Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eq., 31, 53-98 (1979)
8. Haken, H.: Synergetics, An Introduction, Springer 1983
9. Heinrich, R., Schuster, S.: The Regulation of Cellular Systems, New York: Chapman & Hall 1996
10. Jay, L.O., Sandu, A., Potra, F.A., Carmichael, G.R.: Improved quasi-steady-state approximation methods for atmospheric chemistry integration, SIAM J. Sci. Comput., 18, 182-202 (1997)
11. Kevorkian, J., Cole, J.D.: Perturbation Methods in Applied Mathematics, Springer 1981
12. Kuby, S.A.: A Study of Enzymes. I. Enzyme Catalysis, Kinetics, and Substrate Binding, CRC Press 1991
13. Lefever, R., Nicolis, G., Borckmans, P.: The Brusselator: It does oscillate all the same, J. Chem. Soc., Faraday Trans. I, 84, 1013-1023 (1988)
14. Maini, P.K., Burke, Meghan, A., Murray, J.D.: On the quasi-steady-state assumption applied to Michaelis-Menten and suicide substrate reactions with diffusion, Phil. Trans. R. Soc. Lond. A, 337, 299-306 (1991)
15. Murray, J.D.: Asymptotic Analysis, Springer 1984
16. Olver, F.W.J.: Introduction to Asymptotics and Special Functions, Academic Press 1974
17. Peters, N., Rogg, B., Eds.: Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer 1993
18. Pota, G.: Two-component bimolecular systems cannot have limit cycles: A complete proof, J. Chem. Phys., 78, 1621-1622 (1983)
19. Schauer, M., Heinrich, R.: Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks, J. Math. Biosci., 65, 155-170 (1983)
20. Segel, L.A.: On the validity of the steady state assumption of enzyme kinetics, Bull. Math. Biol., 50, 579-593 (1988)
21. Segel, L.A., Slemrod, M.: The quasi-steady-state assumption: A case study in perturbation, SIAM Rev., 31, 446-477 (1989)
22. Stiefenhofer, M.: Quasi-steady-state approximation for chemical reaction networks, J. Math. Biol., 36, 593-609 (1998)
23. Tichonov, A.N.: Systems of differential equations, which contain small parameters before the derivatives, (in russian), Mat. Sbornik, 31, 575-586 (1952)
24. Vasil'eva, A.B., Butuzov, V.F., Kalachev, L.V.: The Boundary Function Method for Singular Perturbation Problems, SIAM 1995