000 03752nam a22004695i 4500
001 978-1-4419-7646-8
003 DE-He213
005 20140220083724.0
007 cr nn 008mamaa
008 100929s2011 xxu| s |||| 0|eng d
020 _a9781441976468
_9978-1-4419-7646-8
024 7 _a10.1007/978-1-4419-7646-8
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aSmith, Hal.
_eauthor.
245 1 3 _aAn Introduction to Delay Differential Equations with Applications to the Life Sciences
_h[electronic resource] /
_cby Hal Smith.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXI, 172 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v57
505 0 _a1 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 _aThis 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 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aBiology
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical Biology in General.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441976451
830 0 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v57
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-7646-8
912 _aZDB-2-SMA
999 _c105822
_d105822