Multiple Time Scale Dynamics

Christian Kuehn (Autor)

Buch | Hardcover

XIII, 814 Seiten

2015
Springer International Publishing (Verlag)
978-3-319-12315-8 (ISBN)

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This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

Christian Kuehn is a Postdoctoral Researcher at Vienna University of Technology, Institute for Analysis and Scientific Computing in Vienna, Austria. He received his PhD in Applied Mathematics from Cornell University in 2010. His research areas include: applied mathematics, differential equations, dynamical systems, numerical mathematics, and stochastics.

Introduction.- General Fenichel Theory.- Geometric Singular Perturbation Theory.- Normal Forms.- Direct Asymptotic Methods.- Tracking Invariant Manifolds.- The Blow-Up Method.- Singularities and Canards.- Advanced Asymptotic Methods.- Numerical Methods.- Computing Manifolds.- Scaling and Delay.- Oscillations.- Chaos in Fast-Slow Systems.- Stochastic Systems.- Topological Methods.- Spatial Dynamics.- Infinite Dimensions.- Other Topics.- Applications.

"It merges a wide variety of different mathematical techniques into a more unified framework. ... this is a very interesting introduction to multiscale dynamics which will be of much assistance to both students and researchers. The target audience of this book is senior undergraduates and graduate students as well as researchers interested in using the theory of multiple time scale dynamics in nonlinear science, either from a theoretical or a mathematical modeling perspective." (Tewfik Sari, Mathematical Reviews, May, 2016)

"This interesting monograph is a self-contained, coherent overview of the backgrounds and progress of the dynamical systems with multiple time scales. ... The book contains excellent mathematics and is a well-written and unique source of information on the multiple time scale dynamics. I highly recommend it to all researchers and graduate students who would like to understand the geometric singular perturbation theory." (Robert Vrabel, zbMATH 1335.34001, 2016)

Erscheint lt. Verlag	6.3.2015
Reihe/Serie	Applied Mathematical Sciences
Zusatzinfo	XIII, 814 p. 196 illus., 48 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	795 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Bifurcations • Canards • Fast-Slow Systems • Geometric Singular Perturbation Theory • invariant manifolds • Mixed-mode Oscillations • Multiple Time Scales • Normal Hyperbolicity • Ordinary differential equations
ISBN-10	3-319-12315-7 / 3319123157
ISBN-13	978-3-319-12315-8 / 9783319123158
Zustand	Neuware