Singular Perturbations

Introduction to System Order Reduction Methods with Applications

  • Elena Shchepakina
  • Vladimir Sobolev
  • Michael P. Mortell

Part of the Lecture Notes in Mathematics book series (LNM, volume 2114)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 1-23
  3. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 25-42
  4. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 43-80
  5. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 81-92
  6. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 93-110
  7. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 111-117
  8. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 119-139
  9. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 141-182
  10. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
    Pages 183-198
  11. Back Matter
    Pages 199-214

About this book

Introduction

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level.

Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system.

Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.

Keywords

Black Swans Canards Chemical Kinetics Combustion and Explosion Enzyme Kinetics Integral Manifolds Invariant Manifolds Laser and Reacting System Manipulators Singular Perturbations System Order Reduction

Authors and affiliations

  • Elena Shchepakina
    • 1
  • Vladimir Sobolev
    • 2
  • Michael P. Mortell
    • 3
  1. 1.Samara State Aerospace UniversitySamaraRussia
  2. 2.Samara State Aerospace UniversitySamaraRussia
  3. 3.University College CorkCorkIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-09570-7
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-09569-1
  • Online ISBN 978-3-319-09570-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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