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Look Inside Biological Delay Systems

Biological Delay Systems
Linear Stability Theory

AUD$187.95 inc GST

Part of Cambridge Studies in Mathematical Biology

  • Date Published: May 1989
  • availability: Available
  • format: Hardback
  • isbn: 9780521340847

AUD$ 187.95 inc GST
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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.

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    Product details

    • Date Published: May 1989
    • format: Hardback
    • isbn: 9780521340847
    • length: 248 pages
    • dimensions: 216 x 140 x 17 mm
    • weight: 0.46kg
    • availability: Available
  • 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.

  • Author

    N. MacDonald, University of Glasgow

    Editors

    C. Cannings

    Frank C. Hoppensteadt

    Lee A. Segel

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