Multiple Time Scale Dynamics [electronic resource] / by Christian Kuehn.

By: Kuehn, Christian [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Applied Mathematical Sciences: 191Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Description: XIII, 814 p. 196 illus., 48 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319123165Subject(s): Mathematics | Dynamics | Ergodic theory | Differential equations | Computer mathematics | Probabilities | Physics | Mathematics | Dynamical Systems and Ergodic Theory | Theoretical, Mathematical and Computational Physics | Computational Mathematics and Numerical Analysis | Ordinary Differential Equations | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No titleDDC classification: 515.39 | 515.48 LOC classification: QA313Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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. .
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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.

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. .

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