Overview
- Center manifold reduction & computation of normal forms is applied; normal forms for bifurcations of limit cycles
- More results on topological equivalence of scalar maps are given
- Techniques to study delay differential equations including Hopf bifurcation are presented
Part of the book series: Applied Mathematical Sciences (AMS, volume 112)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations.
The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used.
This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis.
From reviews of earlier editions:
"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
"It is both a toolkit and a primer" - UK Nonlinear News
Authors and Affiliations
Bibliographic Information
Book Title: Elements of Applied Bifurcation Theory
Authors: Yuri A. Kuznetsov
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-031-22007-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-22006-7Published: 19 April 2023
Softcover ISBN: 978-3-031-22009-8Published: 19 April 2024
eBook ISBN: 978-3-031-22007-4Published: 18 April 2023
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 4
Number of Pages: XXVI, 703
Number of Illustrations: 287 b/w illustrations
Topics: Dynamical Systems and Ergodic Theory, Ordinary Differential Equations, Applications of Mathematics