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Biological Delay Systems : Linear Stability Theory - N. Macdonald

Biological Delay Systems

Linear Stability Theory

By: N. Macdonald, C. Cannings (Editor), Frank C. Hoppensteadt (Editor), Lee A. Segel (Editor)

Hardcover Published: 11th December 2003
ISBN: 9780521340847
Number Of Pages: 248

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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. Much of the material is based on recent research and appears here for the first time in book form. Yet the work not only is a synthesis of this research but also an exposition suited for courses; exercises are provided at the end of each chapter. Thus it will be appreciated by graduate students and research workers in mathematical biology, control theory and population dynamics.

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
Solutions to exercises
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521340847
ISBN-10: 0521340845
Series: Cambridge Studies in Mathematical Biology
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 248
Published: 11th December 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 21.6 x 13.8  x 1.7
Weight (kg): 0.49

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