
Elements of applied bifurcation theory / Yuri A. Kuznetsov.
id 99127175459606421
Elements of Applied Bifurcation Theory / Yuri A. Kuznetsov.
 Format
 Book
 Language
 English
 Εdition
 Fourth edition.
 Published/Created

 Cham, Switzerland : Springer, 2023.
 ©2004
 Description
 1 online resource (XXVI, 703 p. 287 illus.)
Details
 Subject(s)
 Series

 Applied mathematical sciences (SpringerVerlag New York Inc.) ; Volume 112. [More in this series]
 Applied Mathematical Sciences Series ; Volume 112
 Summary note
 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 .
 Bibliographic references
 Includes bibliographical references and index.
 Source of description
 Description based on print version record.
 Contents

 1 Introduction to Dynamical Systems
 2 Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
 3 OneParameter Bifurcations of Equilibria in ContinuousTime Dynamical Systems
 4 OneParameter Bifurcations of Fixed Points in DiscreteTime Dynamical Systems
 5 Bifurcations of Equilibria and Periodic Orbits in nDimensional Dynamical Systems
 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria
 7 Other OneParameter Bifurcations in ContinuousTime Dynamical Systems
 8 TwoParameter Bifurcations of Equilibria in ContinuousTime Dynamical Systems
 9 TwoParameter Bifurcations of Fixed Points in DiscreteTime 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.
 ISBN
 3031220072
 Doi
 10.1007/9783031220074
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