Kuznetsov Elements of Applied Bifurcation Theory

Erscheinungsjahr 2013
ISBN: 978-1-4757-2421-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 112, 518 Seiten, eBook

Reihe: Applied Mathematical Sciences

During the last few years several good textbooks on nonlinear dynamics have ap peared for graduate students in applied mathematics. It seems, however, that the majority of such books are still too theoretically oriented and leave many practi cal issues unclear for people intending to apply the theory to particular research problems. This book is designed for advanced undergraduate or graduate students in mathematics who will participate in applied research. It is also addressed to professional researchers in physics, biology, engineering, and economics who use dynamical systems as modeling tools in their studies. Therefore, only a moderate mathematical background in geometry, linear algebra, analysis, and differential equations is required. A brief summary of general mathematical terms and results that are assumed to be known in the main text appears at the end of the book. Whenever possible, only elementary mathematical tools are used. For example, we do not try to present normal form theory in full generality, instead developing only the portion of the technique sufficient for our purposes. The book aims to provide the student (or researcher) with both a solid basis in dynamical systems theory and the necessary understanding of the approaches, methods, results, and terminology used in the modem applied mathematics litera ture. A key theme is that of topological equivalence and codimension, or "what one may expect to occur in the dynamics with a given number of parameters allowed to vary.

Zielgruppe

Research

Autoren/Hrsg.

Kuznetsov, Yuri A.

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 Systems.- 4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems.- 5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems.- 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- 7 Other One-Parameter Bifurcations in Continuous-Time 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.2 Analysis.- A.3 Geometry.- References.