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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)
Resource Information
The item An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 wellposedness 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 PoincareBendixson theory for monotone cyclic feedback systems, obtained by MalletParet 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.
 Language

 eng
 eng
 Edition
 1st ed. 2011.
 Extent
 1 online resource (177 p.)
 Note
 Description based upon print version of record
 Contents

 1 Introduction.The Simplest Delay Equation.Delayed Negative Feedback: A WarmUp
 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
 Isbn
 9781441976468
 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
 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 wellposedness 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 PoincareBendixson theory for monotone cyclic feedback systems, obtained by MalletParet 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.
 http://library.link/vocab/creatorName
 smith, hal
 Dewey number
 515.353
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 dHsnJDCMsKI
 Language note
 English
 LC call number
 QA370380
 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)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 167170) 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 WarmUp  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
 10.1007/9781441976468
 Specific material designation
 remote
 System control number

 (CKB)2670000000045317
 (EBL)3065921
 (SSID)ssj0000449729
 (PQKBManifestationID)11284721
 (PQKBTitleCode)TC0000449729
 (PQKBWorkID)10429608
 (PQKB)11627884
 (DEHe213)9781441976468
 (MiAaPQ)EBC3065921
 (EXLCZ)992670000000045317
 Label
 An Introduction to Delay Differential Equations with Applications to the Life Sciences, by hal smith, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 167170) 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 WarmUp  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
 10.1007/9781441976468
 Specific material designation
 remote
 System control number

 (CKB)2670000000045317
 (EBL)3065921
 (SSID)ssj0000449729
 (PQKBManifestationID)11284721
 (PQKBTitleCode)TC0000449729
 (PQKBWorkID)10429608
 (PQKB)11627884
 (DEHe213)9781441976468
 (MiAaPQ)EBC3065921
 (EXLCZ)992670000000045317
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