Elements of Applied Bifurcation Theory

3rd Auflage 2004
ISBN: 978-0-387-21906-6
Verlag: Springer

Buch, Englisch, Band 112, 632 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1144 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Kuznetsov, Yuri

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

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.