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Biological Delay Systems Linear Stability Theory

ISBN-10: 0521048168

ISBN-13: 9780521048163

Edition: N/A

Authors: N. MacDonald, C. Cannings, Frank C. Hoppensteadt, Lee A. Segel

List price: $129.99
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Description:

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 populations 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.
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Book details

List price: $129.99
Publisher: Cambridge University Press
Publication date: 1/3/2008
Binding: Paperback
Pages: 248
Size: 5.43" wide x 8.50" long x 0.63" tall
Weight: 0.682
Language: English

Lee A. Segel (1932-2005) was a Professor at the Weizmann Institute of Science, Rehovot, Israel, where he served as Chairman of Applied Mathematics, Dean of Mathematical Sciences and Chairman of the Scientific Council. He was an Ulam Scholar at the Los Alamos National Laboratory, a Fellow of the American Association for the Advancement of Science and a member of the Santa Fe Institute, where he continued his work on complex adaptive systems. He served as editor or editorial board member of six journals.

Preface
How delays arise and what effects they have
Ordinary differential equations: the polynomial characteristic equation
Functional differential equations: the transcendental characteristic equation
Hurwitz polynomials
First- and second-order systems with a discrete delay
Higher-order systems, and systems with two delays
Reducing a discrete delay problem to one with a polynomial characteristic equation
Stability independent of delay
Distributed delay
Reducible delays and linear subsystems
Appendices
Solutions to exercises