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

  • Hal┬áSmith
Book
Part of the Texts in Applied Mathematics book series (TAM, volume 57)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Hal Smith
    Pages 1-11
  3. Hal Smith
    Pages 13-24
  4. Hal Smith
    Pages 25-39
  5. Hal Smith
    Pages 41-59
  6. Hal Smith
    Pages 87-118
  7. Hal Smith
    Pages 131-147
  8. Back Matter
    Pages 171-172

About this book

Introduction

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a good background in ordinary differential equations and would like to learn about the applications. It may also be of interest to applied mathematicians, computational scientists, and engineers. It focuses on key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models. Aside from standard well-posedness results for the initial value problem, it focuses on stability of equilibria via linearization and Lyapunov functions and on Hopf bifurcation. It contains a brief introduction to abstract dynamical systems focused on those generated by delay equations, introducing limit sets and their properties. Differential inequalities play a significant role in applications and are treated here, along with an introduction to monotone systems generated by delay equations. The book contains some quite recent results such as the Poincare-Bendixson theory for monotone cyclic feedback systems, obtained by Mallet-Paret and Sell. The linear chain trick for a special family of infinite delay equations is treated. The book is distinguished by the wealth of examples that are introduced and treated in detail. These include the delayed logistic equation, delayed chemostat model of microbial growth, inverted pendulum with delayed feedback control, a gene regulatory system, and an HIV transmission model. An entire chapter is devoted to the interesting dynamics exhibited by a chemostat model of bacteriophage parasitism of bacteria. The book has a large number of exercises and illustrations. Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University. 

Keywords

Delay differential equations functional differential equations time delay

Authors and affiliations

  • Hal┬áSmith
    • 1
  1. 1., School of Mathematical and Statistical SArizona State UniversityTempeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7646-8
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7645-1
  • Online ISBN 978-1-4419-7646-8
  • Series Print ISSN 0939-2475
  • About this book