東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Geometric singular perturbation theo...

Wechselberger, Martin.

Linked to FindBook

Google Book

Amazon

博客來

Geometric singular perturbation theory beyond the standard form

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric singular perturbation theory beyond the standard form/ by Martin Wechselberger.
Author:	Wechselberger, Martin.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	x, 137 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Motivating examples -- A coordinate-independent setup for GSPT -- Loss of normal hyperbolicity -- Relaxation oscillations in the general setting -- Pseudo singularities & canards -- What we did not discuss.
Contained By:	Springer eBooks
Subject:	Singular perturbations (Mathematics) -
Online resource:	https://doi.org/10.1007/978-3-030-36399-4
ISBN:	9783030363994

Geometric singular perturbation theory beyond the standard form
Wechselberger, Martin.

Geometric singular perturbation theory beyond the standard form[electronic resource] /by Martin Wechselberger. - Cham :Springer International Publishing :2020. - x, 137 p. :ill., digital ;24 cm. - Frontiers in applied dynamical systems: reviews and tutorials,v.62364-4532 ;. - Frontiers in applied dynamical systems: reviews and tutorials ;v.6..

Introduction -- Motivating examples -- A coordinate-independent setup for GSPT -- Loss of normal hyperbolicity -- Relaxation oscillations in the general setting -- Pseudo singularities & canards -- What we did not discuss.

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT) It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.

ISBN: 9783030363994

Standard No.: 10.1007/978-3-030-36399-4doiSubjects--Topical Terms:

897295
Singular perturbations (Mathematics)

LC Class. No.: QA372 / .W434 2020

Dewey Class. No.: 515.392

Geometric singular perturbation theory beyond the standard form
LDR:02711nmm a2200337 a 4500 001 2216467
003 DE-He213
005 20200721142352.0
006 m d
007 cr nn 008maaau
008 201120s2020 sz s 0 eng d
020 $a 9783030363994 $q (electronic bk.)
020 $a 9783030363987 $q (paper)
024 7 $a 10.1007/978-3-030-36399-4 $2 doi
035 $a 978-3-030-36399-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA372 $b .W434 2020
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBWR $2 thema
082 0 4 $a 515.392 $2 23
090 $a QA372 $b .W386 2020
100 1 $a Wechselberger, Martin. $3 3448823
245 1 0 $a Geometric singular perturbation theory beyond the standard form $h [electronic resource] / $c by Martin Wechselberger.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a x, 137 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in applied dynamical systems: reviews and tutorials, $x 2364-4532 ; $v v.6
505 0 $a Introduction -- Motivating examples -- A coordinate-independent setup for GSPT -- Loss of normal hyperbolicity -- Relaxation oscillations in the general setting -- Pseudo singularities & canards -- What we did not discuss.
520 $a This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT) It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
650 0 $a Singular perturbations (Mathematics) $3 897295
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Ordinary Differential Equations. $3 891264
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Frontiers in applied dynamical systems: reviews and tutorials ; $v v.6. $3 3448824
856 4 0 $u https://doi.org/10.1007/978-3-030-36399-4
950 $a Mathematics and Statistics (Springer-11649)