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Elements of Applied Bifurcation Theory - Yuri A. Kuznetsov

Elements of Applied Bifurcation Theory

Buch | Softcover
XXVI, 703 Seiten
2024 | 4th ed. 2023
Springer International Publishing (Verlag)
978-3-031-22009-8 (ISBN)
CHF 249,95 inkl. MwSt
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 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

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 FredholmAlternative 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.

Erscheinungsdatum
Reihe/Serie Applied Mathematical Sciences
Zusatzinfo XXVI, 703 p. 287 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Schlagworte Applied mathematics • Bifurcation • Dynamical Systems • Mathematica • Numerical analysis • numerical method • Ordinary differential equations • stability
ISBN-10 3-031-22009-9 / 3031220099
ISBN-13 978-3-031-22009-8 / 9783031220098
Zustand Neuware
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