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20140310151445.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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100929s2011 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781441976468 |
|
978-1-4419-7646-8 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA370-380 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.353 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
New York, NY : |
| -- |
Springer New York, |
| -- |
2011. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Smith, Hal. |
| Relator term |
author. |
| 245 13 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
An Introduction to Delay Differential Equations with Applications to the Life Sciences |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Hal Smith. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XI, 172 p. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Texts in Applied Mathematics, |
| International Standard Serial Number |
0939-2475 ; |
| Volume number/sequential designation |
57 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Differential equations, partial. |
|
|---|
| Topical term or geographic name as entry element |
Biology |
| General subdivision |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Partial Differential Equations. |
|
|---|
| Topical term or geographic name as entry element |
Mathematical Biology in General. |
|
|---|
| Topical term or geographic name as entry element |
Applications of Mathematics. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9781441976451 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4419-7646-8 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
