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Nonlinear Dynamics in Physiology and Medicine

  • Textbook
  • © 2003

Overview

Editors:
  1. Anne Beuter

    1. Institut de Biologie, Universite de Montpellier 1, Montpellier Cedex 1, France

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  2. Leon Glass

    1. Department of Physiology, McGill University, Montreal, Canada

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  3. Michael C. Mackey

    1. Department of Physiology, McGill University, Montreal, Canada

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  4. Michèle S. Titcombe

    1. Department of Physiology, McGill University, Montreal, Canada

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Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 25)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xxvi
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  2. Theoretical Approaches in Physiology

    • Michael C. Mackey, Anne Beuter
    Pages 1-7

  3. Introduction to Dynamics in Nonlinear Difference and Differential Equations

    • Jacques Bélair, Leon Glass
    Pages 9-39

  4. Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems

    • Michael R. Guevara
    Pages 41-85

  5. Dynamics of Excitable Cells

    • Michael R. Guevara
    Pages 87-121

  6. Resetting and Entraining Biological Rhythms

    • Leon Glass
    Pages 123-148

  7. Effects of Noise on Nonlinear Dynamics

    • André Longtin
    Pages 149-189

  8. Reentry in Excitable Media

    • Marc Courtemanche, Alain Vinet
    Pages 191-232

  9. Cell Replication and Control

    • Michael C. Mackey, Caroline Haurie, Jacques Bélair
    Pages 233-269

  10. Pupil Light Reflex: Delays and Oscillations

    • John Milton
    Pages 271-301

  11. Data Analysis and Mathematical Modeling of Human Tremor

    • Anne Beuter, Roderick Edwards, Michèle S. Titcombe
    Pages 303-355

  12. Back Matter

    Pages 357-435
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Keywords

About this book

Je tiens impossible de connaître les parties sans connaître le tout, non plus que de connaître le tout sans connaître particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati­ cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per­ spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra­ ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduatelevel) to a research re­ source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.

Reviews

From the reviews:

"As part of the Springer Interdisciplinary Applied Mathematics Series, this book joins a line of books that are leading the way in showing how mathematics can be usefully applied to biology and physiology." - Bulletin of the AMS, 2004

"This book is an excellent addition to the literature. Perhaps its greatest value is its appeal to a wide class of prospective readers who may range from the biologist (mathematician) who has a mild interest in mathematics (biology) to the researcher who works in one of the fields discussed. … There is a large bibliography, and there are analytical and computer exercises at the end of each chapter." (Jane Cronin, Zentralblatt MATH, Vol. 1050, 2005)

"The book «Nonlinear Dynamics in Physiology and Medicine» is a multi-author effort. … Each chapter is well grounded … . The book’s references list is thorough and valid … . This book is aimed at all scientists studying physiological systems in general … . It fits into curricula usually offered by bio-engineering departments and - happily more and more - also medical schools. … a book of high standards and is to be recommended. It is a title worth possessing as a collection of valuable reference material … ." (Prof. dr. sc. Vladimir Medved, IFMBE News, Vol. 69, November/December, 2004)

"Beuter, Glass, Mackey and Titcombe edit a book that provides an understanding of the theory and application of mathematical tools to the study of physiological systems. The book will be of interest to those involved in the modeling of such physiological systems. … The material is well written, clear and concise. … I liked the book. It makes an important contribution to the field … . I recommend this book. It makes a worthwhile addition to a biological/medical science library." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 91, 2004)

 

Editors and Affiliations

  • Institut de Biologie, Universite de Montpellier 1, Montpellier Cedex 1, France

    Anne Beuter

  • Department of Physiology, McGill University, Montreal, Canada

    Leon Glass, Michael C. Mackey, Michèle S. Titcombe

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