Skip to main content
SpringerLink
Log in
Book cover

Elements of Applied Bifurcation Theory

  • Book
  • © 2004

Overview

Authors:
  1. Yuri A. Kuznetsov

    1. Department of Mathematics, Utrecht University, Utrecht, The Netherlands
      Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Mathematical Sciences (AMS, volume 112)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages I-XXII
    Download chapter PDF

  2. Introduction to Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 1-37

  3. Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 39-76

  4. One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 77-115

  5. One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 117-155

  6. Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 157-194

  7. Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria

    • Yuri A. Kuznetsov
    Pages 195-247

  8. Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 249-294

  9. Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 295-405

  10. Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems

    • Yuri A. Kuznetsov
    Pages 407-504

  11. Numerical Analysis of Bifurcations

    • Yuri A. Kuznetsov
    Pages 505-585

  12. Back Matter

    Pages 587-634
    Download chapter PDF
Back to top

Keywords

About this book

The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri­ ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder­ ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.

Reviews

Review of earlier edition

"I know of no other book that so clearly explains the basic phenomena of bifurcation theory." Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." Bulletin of the AMS

From the reviews of the third edition:

"In the third edition of this textbook, the material again has been slightly extended while the main structure of the book was kept. … the clear structure of the book allows applied scientists to use it as a reference book. … Kuznetsov’s book on applied bifurcation theory is still very useful both as a textbook and as a reference work for researchers from the natural sciences, engineering or economics." (Jörg Härterich, Zentralblatt MATH, Vol. 1082, 2006)

“This book deals with the theory ofdynamical systems relevant for applications. The material is presented in a systematic and very readable form. It covers recent developments in bifurcation theory, with special attention to efficient numerical implementations. The text aims at an audience of graduate and Ph.D. students in applied mathematics, and researchers in science and engineering, who use dynamical systems and bifurcation analysis as a tool. Each chapter contains useful examples and many illustrations.” (Dirk Roose, Bulletin of the Belgian Mathematical Society, 2007)

Authors and Affiliations

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

    Yuri A. Kuznetsov

  • Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, Russia

    Yuri A. Kuznetsov

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation