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Elements of Applied Bifurcation Theory

  • Yuri A. Kuznetsov

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

About this book

Introduction

During the last few years several good textbooks on nonlinear dynamics have ap­ peared for graduate students in applied mathematics. It seems, however, that the majority of such books are still too theoretically oriented and leave many practi­ cal issues unclear for people intending to apply the theory to particular research problems. This book is designed for advanced undergraduate or graduate students in mathematics who will participate in applied research. It is also addressed to professional researchers in physics, biology, engineering, and economics who use dynamical systems as modeling tools in their studies. Therefore, only a moderate mathematical background in geometry, linear algebra, analysis, and differential equations is required. A brief summary of general mathematical terms and results that are assumed to be known in the main text appears at the end of the book. Whenever possible, only elementary mathematical tools are used. For example, we do not try to present normal form theory in full generality, instead developing only the portion of the technique sufficient for our purposes. The book aims to provide the student (or researcher) with both a solid basis in dynamical systems theory and the necessary understanding of the approaches, methods, results, and terminology used in the modem applied mathematics litera­ ture. A key theme is that of topological equivalence and codimension, or "what one may expect to occur in the dynamics with a given number of parameters allowed to vary.

Keywords

Bifurcation Theory Mathematica applied mathematics bifurcation biology design dynamical systems implementation model online stability system systems theory techniques tool

Authors and affiliations

  • Yuri A. Kuznetsov
    • 1
    • 2
  1. 1.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands
  2. 2.Institute of Mathematical Problems of BiologyRussian Academy of SciencesPushchino, Moscow RegionRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2421-9
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2423-3
  • Online ISBN 978-1-4757-2421-9
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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