The Resource An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource)

An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource)

Label
An Introduction to Delay Differential Equations with Applications to the Life Sciences
Title
An Introduction to Delay Differential Equations with Applications to the Life Sciences
Statement of responsibility
by hal smith
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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.
Member of
Is Subseries of
http://library.link/vocab/creatorName
smith, hal
Dewey number
515.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
dHsnJDCMsKI
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Texts in Applied Mathematics,
Series volume
57
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Mathematics
  • Partial Differential Equations
  • Mathematical and Computational Biology
  • Applications of Mathematics
Label
An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 167-170) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
1 Introduction.-The Simplest Delay Equation.-Delayed Negative Feedback: A Warm-Up -- Existence of Solutions -- Linear Systems and Linearization -- Semidynamical Systems and Delay Equations -- Hopf Bifurcation -- Distributed Delay Equations and the Linear Chain Trick -- Phage and Bacteria in a Chemostat.-References -- Index
Dimensions
unknown
Edition
1st ed. 2011.
Extent
1 online resource (177 p.)
Form of item
online
Isbn
9781441976468
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-7646-8
Specific material designation
remote
System control number
  • (CKB)2670000000045317
  • (EBL)3065921
  • (SSID)ssj0000449729
  • (PQKBManifestationID)11284721
  • (PQKBTitleCode)TC0000449729
  • (PQKBWorkID)10429608
  • (PQKB)11627884
  • (DE-He213)978-1-4419-7646-8
  • (MiAaPQ)EBC3065921
  • (EXLCZ)992670000000045317
Label
An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 167-170) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
1 Introduction.-The Simplest Delay Equation.-Delayed Negative Feedback: A Warm-Up -- Existence of Solutions -- Linear Systems and Linearization -- Semidynamical Systems and Delay Equations -- Hopf Bifurcation -- Distributed Delay Equations and the Linear Chain Trick -- Phage and Bacteria in a Chemostat.-References -- Index
Dimensions
unknown
Edition
1st ed. 2011.
Extent
1 online resource (177 p.)
Form of item
online
Isbn
9781441976468
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-7646-8
Specific material designation
remote
System control number
  • (CKB)2670000000045317
  • (EBL)3065921
  • (SSID)ssj0000449729
  • (PQKBManifestationID)11284721
  • (PQKBTitleCode)TC0000449729
  • (PQKBWorkID)10429608
  • (PQKB)11627884
  • (DE-He213)978-1-4419-7646-8
  • (MiAaPQ)EBC3065921
  • (EXLCZ)992670000000045317

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