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An Introduction to Delay Differential Equations with Applications to the Life Sciences

  • Textbook
  • © 2011

Overview

Authors:
  1. Hal Smith

    1. , School of Mathematical and Statistical S, Arizona State University, Tempe, USA

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  • Focuses on key tools to understand delay equations
  • Begins with a survey of mathematical models involving delay equations
  • Wealth of examples, exercises and illustrations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Applied Mathematics (TAM, volume 57)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Hal Smith
    Pages 1-11

  3. Delayed Negative Feedback: A Warm-Up

    • Hal Smith
    Pages 13-24

  4. Existence of Solutions

    • Hal Smith
    Pages 25-39

  5. Linear Systems and Linearization

    • Hal Smith
    Pages 41-59

  6. Semidynamical Systems and Delay Equations

    • Hal Smith
    Pages 61-85

  7. Hopf Bifurcation

    • Hal Smith
    Pages 87-118

  8. Distributed Delay Equations and the Linear Chain Trick

    • Hal Smith
    Pages 119-130

  9. Phage and Bacteria in a Chemostat

    • Hal Smith
    Pages 131-147

  10. Back Matter

    Pages 171-172
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Keywords

About this book

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.

Reviews

From the reviews:

“This text is designed to be an introduction to the theory of differential equations with delay for advanced undergraduates and beginning graduate students.” (William J. Satzer, The Mathematical Association of America, November, 2010)

“This textbook would serve as an excellent reference text to help a mathematics faculty develop an introductory mathematics course on DDEs … . This textbook clearly places the study of DDEs firmly within the standard curriculum of a graduate program in mathematics and well within the scope of a strong final-year undergraduate mathematics major. … this text will have a positive impact on biomathematics education and be a welcome addition. We certainly find it so.” (John G. Milton and Michael C. Mackey, Mathematical Reviews, Issue 2011 k)

“This book gives a first introduction to delay differential equations that is intended for mathematics students. Thanks to the emphasis on applications to life sciences, it can be recommended also to scientists from this discipline that wish to get a deeper understanding of the theoretical aspects for this widely used class of models.” (Matthias Wolfrum, Zentralblatt MATH, Vol. 1227, 2012)

Authors and Affiliations

  • , School of Mathematical and Statistical S, Arizona State University, Tempe, USA

    Hal Smith

About the author

Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University.

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