Zum Hauptinhalt springen
Dekorationsartikel gehören nicht zum Leistungsumfang.
Elements of Applied Bifurcation Theory
Buch von Yuri A. Kuznetsov
Sprache: Englisch

181,89 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Aktuell nicht verfügbar

Kategorien:
Beschreibung
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
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
Zusammenfassung

From Reviews of the First Edition: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory." -Mathematical Reviews

This book provides a student or researcher with a solid basis in nonlinear dynamical systems and their bifurcations, giving them the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature. It covers the basic topics of the bifurcation theory and can help in composing a course on nonlinear dynamical systems or system theory. This new edition preserves the structure of the previous edition, while updating the context to incorporate recent theoretical and software developments, in particular new and improved numerical methods for bifurcation analysis.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Applied Mathematical Sciences
Inhalt: xxvi
703 S.
287 s/w Illustr.
703 p. 287 illus.
ISBN-13: 9783031220067
ISBN-10: 3031220064
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kuznetsov, Yuri A.
Auflage: 4th ed. 2023
Hersteller: Springer International Publishing
Springer International Publishing AG
Applied Mathematical Sciences
Maße: 241 x 160 x 45 mm
Von/Mit: Yuri A. Kuznetsov
Erscheinungsdatum: 19.04.2023
Gewicht: 1,25 kg
Artikel-ID: 125731258
Zusammenfassung

From Reviews of the First Edition: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory." -Mathematical Reviews

This book provides a student or researcher with a solid basis in nonlinear dynamical systems and their bifurcations, giving them the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature. It covers the basic topics of the bifurcation theory and can help in composing a course on nonlinear dynamical systems or system theory. This new edition preserves the structure of the previous edition, while updating the context to incorporate recent theoretical and software developments, in particular new and improved numerical methods for bifurcation analysis.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Applied Mathematical Sciences
Inhalt: xxvi
703 S.
287 s/w Illustr.
703 p. 287 illus.
ISBN-13: 9783031220067
ISBN-10: 3031220064
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kuznetsov, Yuri A.
Auflage: 4th ed. 2023
Hersteller: Springer International Publishing
Springer International Publishing AG
Applied Mathematical Sciences
Maße: 241 x 160 x 45 mm
Von/Mit: Yuri A. Kuznetsov
Erscheinungsdatum: 19.04.2023
Gewicht: 1,25 kg
Artikel-ID: 125731258
Warnhinweis

Ähnliche Produkte

Ähnliche Produkte