Practical Bifurcation and Stability Analysis

  • Rüdiger Seydel

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 5)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Rüdiger Seydel
    Pages 1-52
  3. Rüdiger Seydel
    Pages 53-115
  4. Rüdiger Seydel
    Pages 117-167
  5. Rüdiger Seydel
    Pages 169-198
  6. Rüdiger Seydel
    Pages 303-356
  7. Rüdiger Seydel
    Pages 357-384
  8. Rüdiger Seydel
    Pages 385-423
  9. Back Matter
    Pages 1-57

About this book

Introduction

This book covers the central role that bifurcations play in nonlinear phenomena, explaining mechanisms of how stability is gained or lost. It emphasizes practical and computational methods for analyzing dynamical systems. A wide range of phenomena between equilibrium and chaos is explained and illustrated by examples from science and engineering. The book is a practical guide for performing parameter studies and includes exercises.

Combining an introduction on the textbook level with an exposition of computational methods, this book addresses the mathematical needs of scientists and engineers. It should be of interest to those in a wide variety of disciplines, including physics, mechanical engineering, electrical engineering, chemistry and chemical engineering, biology, and medicine. Both graduate students (in courses on dynamical systems, stability analysis, differential equations, and chaos) and professionals will be able to use the book equally well. The introduction avoids mathematical formalism, and the only required background is calculus.

In the third edition there is a chapter on applications and extensions of standard ODE approaches, for example, to delay equations, to differential-algebraic equations, and to reaction-diffusion problems. Additional material is inserted, including the topics deterministic risk, pattern formation, and control of chaos, and many further references.

Review of Earlier Edition:

"The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society

Keywords

Algebra Applied Bifurcation Analysis Equilibrium and Chaos Numerical Algorithms Numerical bifurcation methods Periodic Solutions Practical Bifurcation Stability Analysis Test Functions algorithms calculus chaos ordinary differential equation

Authors and affiliations

  • Rüdiger Seydel
    • 1
  1. 1.Mathematisch-Naturwiss. FakultätUniversität KölnKölnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1740-9
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1739-3
  • Online ISBN 978-1-4419-1740-9
  • Series Print ISSN 0939-6047
  • About this book