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

1. Front Matter

   Pages i-xi

   PDF

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

    PDF

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.

• Delay differential equations
• functional differential equations
• time delay
• partial differential equations

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)

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

  Hal Smith

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

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