Elements of applied bifurcation theory / Yuri A. Kuznetsov.
Kuznet͡sov, I͡U. A. (I͡Uriĭ Aleksandrovich), author.
2023
QA380
Available Online

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Title Elements of applied bifurcation theory / Yuri A. Kuznetsov.
Author Kuznet͡sov, I͡U. A. (I͡Uriĭ Aleksandrovich), author.
Edition Fourth edition.
ISBN 9783031220074 (electronic bk.)
3031220072 (electronic bk.)
9783031220067
3031220064
DOI https://doi.org/10.1007/978-3-031-22007-4
Published Cham : Springer, 2023.
Language English
Description 1 online resource (706 pages) : illustrations (black and white).
Item Number 10.1007/978-3-031-22007-4 doi
Call Number QA380
Dewey Decimal Classification 515/.392
Summary 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 "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. - Bulletin of the Belgian Mathematical Society .
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 112.
Available in Other Form Elements of applied bifurcation theory.
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All Resources
1 Introduction to Dynamical Systems
2 Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems
4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems
5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems
6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria
7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems
8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems
9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems
10 Numerical Analysis of Bifurcations
A Basic Notions from Algebra, Analysis, and Geometry
A.1 Algebra
A.1.1 Matrices
A.1.2 Vector spaces and linear transformations
A.1.3 Eigenvectors and eigenvalues
A.1.4 Invariant subspaces, generalized eigenvectors, and Jordan normal form
A.1.5 Fredholm Alternative Theorem
A.1.6 Groups
A.2 Analysis
A.2.1 Implicit and Inverse Function Theorems
A.2.2 Taylor expansion
A.2.3 Metric, normed, and other spaces
A.3 Geometry
A.3.1 Sets
A.3.2 Maps
A.3.3 Manifolds
References.

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