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  • © 1990

Nonlinear Differential Equations and Dynamical Systems

Part of the book series: Universitext (UTX)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-IX
  2. Introduction

    • Ferdinand Verhulst
    Pages 1-6
  3. Autonomous equations

    • Ferdinand Verhulst
    Pages 7-26
  4. Critical points

    • Ferdinand Verhulst
    Pages 27-38
  5. Periodic solutions

    • Ferdinand Verhulst
    Pages 39-61
  6. Introduction to the theory of stability

    • Ferdinand Verhulst
    Pages 62-72
  7. Linear equations

    • Ferdinand Verhulst
    Pages 73-87
  8. Stability by linearisation

    • Ferdinand Verhulst
    Pages 88-100
  9. Stability analysis by the direct method

    • Ferdinand Verhulst
    Pages 101-116
  10. Introduction to perturbation theory

    • Ferdinand Verhulst
    Pages 117-129
  11. The Poincaré-Lindstedt method

    • Ferdinand Verhulst
    Pages 130-144
  12. The method of averaging

    • Ferdinand Verhulst
    Pages 145-176
  13. Relaxation oscillations

    • Ferdinand Verhulst
    Pages 177-182
  14. Bifurcation theory

    • Ferdinand Verhulst
    Pages 183-203
  15. Chaos

    • Ferdinand Verhulst
    Pages 204-217
  16. Hamiltonian systems

    • Ferdinand Verhulst
    Pages 218-236
  17. Back Matter

    Pages 237-280

About this book

On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research after studying this book.

Authors and Affiliations

  • Department of Mathematics, University of Utrecht, TA Utrecht, The Netherlands

    Ferdinand Verhulst

About the author

Ferdinand Verhulst was born in Amsterdam, The Netherlands, in 1939.

He graduated at the University of Amsterdam in Astrophysics and Mathematics. A period of five years at the Technological University of Delft, started his interest in technological problems, resulting in various cooperations with engineers. His other interests include the methods and applications of asymptotic analysis, nonlinear oscillations and wave theory.

He holds a chair of dynamical systems at the department of mathematics at the University of Utrecht.

Among his other interests are a publishing company, Epsilon Uitgaven, that he founded in 1985, and the relation between dynamical systems and psychoanalysis.

For more information see www.math.uu.nl/people/verhulst

Bibliographic Information

Buy it now

Buying options

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access