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Cambridge Studies in Mathematical Biology #9: Biological Delay Systems: Linear Stability Theory

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Cambridge Studies in Mathematical Biology #9: Biological Delay Systems: Linear Stability Theory Cover

 

Synopses & Reviews

Publisher Comments:

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. This book 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.

Synopsis:

This book deals with a fundamental question in the analysis of the effects of delays, namely whether they affect the stability of steady states.

Table of 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.

Product Details

ISBN:
9780521048163
Author:
Macdonald, N.
Publisher:
Cambridge University Press
Editor:
Cannings, C.
Editor:
Hoppensteadt, Frank C.
Author:
Segel, Lee A.
Author:
Hoppensteadt, Frank C.
Author:
MacDonald, N.
Author:
Cannings, C.
Location:
Cambridge
Subject:
Life Sciences - Anatomy & Physiology
Subject:
Applied
Subject:
Health and Medicine-Anatomy and Physiology
Edition Description:
Trade paper
Series:
Cambridge Studies in Mathematical Biology
Series Volume:
9
Publication Date:
20080131
Binding:
TRADE PAPER
Language:
English
Pages:
248
Dimensions:
8.53x5.47x.63 in. .69 lbs.

Related Subjects

Health and Self-Help » Health and Medicine » Anatomy and Physiology
Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Biology » General
Science and Mathematics » Mathematics » Applied

Cambridge Studies in Mathematical Biology #9: Biological Delay Systems: Linear Stability Theory New Trade Paper
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Product details 248 pages Cambridge University Press - English 9780521048163 Reviews:
"Synopsis" by , This book deals with a fundamental question in the analysis of the effects of delays, namely whether they affect the stability of steady states.
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