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Biological Delay Systems: Linear Stability Theory

Series: Cambridge Studies in Mathematical Biology

By: N MacDonald (Author)

248 pages, b/w illustrations

Cambridge University Press

Paperback | Jan 2008 | #218642 | ISBN-13: 9780521048163
Availability: Usually dispatched within 6 days Details
NHBS Price: £66.99 $84/€80 approx
Hardback | Mar 1989 | #218643 | ISBN: 0521340845
Availability: Usually dispatched within 6 days Details
NHBS Price: £103.00 $130/€123 approx

About this book

In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. Biological Delay Systems is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.


Contents

Preface

1. How delays arise and what effects they have
2. Ordinary differential equations: the polynomial characteristic equation
3. Functional differential equations: the transcendental characteristic equation
4. Hurwitz polynomials
5. First- and second-order systems with a discrete delay
6. Higher-order systems, and systems with two delays
7. Reducing a discrete delay problem to one with a polynomial characteristic equation
8. Stability independent of delay
9. Distributed delay
10. Reducible delays and linear subsystems

Appendices
Solutions to exercises
References
Index


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