Abstract
In this chapter the first number in the title of a section denotes the dimension of the slow variable, the second one denotes the dimension of the fast variable. A series of examples, of increasing complexity, are given to illustrate the theoretical concepts. The main examples come from applications in enzyme kinetics. These examples illustrate the effectiveness of the order reduction method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Johnson, R.S.: Singular Perturbation Theory. Springer, New York (2005)
Mishchenko, E.F., Rozov, N.Kh.: Differential Equations with Small Parameters and Relaxation Oscillations. Plenum Press, New York (1980)
Murray, J.D.: Lectures on Nonlinear Differential Equation Models in Biology. Clarendon Press, Oxford (1977)
Murray, J.D.: Mathematical Biology I. An Introduction. Springer, New York (2001)
Schneider, K.R., Wilhelm, T.: Model reduction by extended quasi-steady state assumption. J. Math. Biology. 40, 443–450 (2000)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Shchepakina, E., Sobolev, V., Mortell, M.P. (2014). The Book of Numbers. In: Singular Perturbations. Lecture Notes in Mathematics, vol 2114. Springer, Cham. https://doi.org/10.1007/978-3-319-09570-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-09570-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09569-1
Online ISBN: 978-3-319-09570-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)