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Elements of Applied Bifurcation Theory [electronic resource] / by Yuri A. Kuznetsov.
Author
Kuznetsov, Yuri A.
[Browse]
Format
Book
Language
English
Εdition
4th ed. 2023.
Published/Created
Cham : Springer International Publishing : Imprint: Springer, 2023.
Description
1 online resource (XXVI, 703 p. 287 illus.)
Availability
Available Online
Springer Nature - Springer Mathematics and Statistics eBooks 2023 English International
Details
Subject(s)
Dynamical systems
[Browse]
Differential equations
[Browse]
Mathematics
[Browse]
Series
Applied Mathematical Sciences, 112
[More in this series]
Applied Mathematical Sciences, 2196-968X ; 112
[More in this series]
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 .
Contents
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.
Show 24 more Contents items
ISBN
3-031-22007-2
Doi
10.1007/978-3-031-22007-4
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Elements of applied bifurcation theory / Yuri A. Kuznetsov.
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99127175459606421