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Time Lags in Biological Models (Paperback, Softcover reprint of the original 1st ed. 1978)
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Time Lags in Biological Models (Paperback, Softcover reprint of the original 1st ed. 1978)
Series: Lecture Notes in Biomathematics, 27
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In many biological models it is necessary to allow the rates of
change of the variables to depend on the past history, rather than
only the current values, of the variables. The models may require
discrete lags, with the use of delay-differential equations, or
distributed lags, with the use of integro-differential equations.
In these lecture notes I discuss the reasons for including lags,
especially distributed lags, in biological models. These reasons
may be inherent in the system studied, or may be the result of
simplifying assumptions made in the model used. I examine some of
the techniques available for studying the solution of the
equations. A large proportion of the material presented relates to
a special method that can be applied to a particular class of
distributed lags. This method uses an extended set of ordinary
differential equations. I examine the local stability of
equilibrium points, and the existence and frequency of periodic
solutions. I discuss the qualitative effects of lags, and how these
differ according to the choice of discrete or distributed lag. The
models studied are drawn from the population dynamiCS of single
species (logistic growth, the chemostat) and of interacting pairs
of species (predation, mutualism), from cell population dynamiCS
(haemopoiesis) and from biochemical kinetics (the Goodwin
oscillator). The last chapter is devoted to a population model
employing difference equations. All these models include non-linear
terms.
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Lecture Notes in Biomathematics, 27 |
Release date: |
November 1978 |
First published: |
1978 |
Authors: |
N. Macdonald
|
Dimensions: |
244 x 170 x 6mm (L x W x T) |
Format: |
Paperback
|
Pages: |
114 |
Edition: |
Softcover reprint of the original 1st ed. 1978 |
ISBN-13: |
978-3-540-09092-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-540-09092-4 |
Barcode: |
9783540090922 |
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