Dynamic Bifurcations

1991
ISBN: 978-3-540-54900-0
Verlag: Springer-Verlag GmbH

Buch, Englisch, Band 1493, 222 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 730 g

Reihe: Lecture Notes in Mathematics

Dynamical Bifurcation Theory is concerned with the phenomena
that occur in one parameter families of dynamical systems
(usually ordinary differential equations), when the
parameter is a slowly varying function of time. During the
last decade these phenomena were observed and studied by
many mathematicians, both pure and applied, from eastern and
western countries, using classical and nonstandard analysis.
It is the purpose of this book to give an account of these
developments. The first paper, by C. Lobry, is an
introduction: the reader will find here an explanation of
the problems and some easy examples; this paper also
explains the role of each of the other paper within the
volume and their relationship to one another.
CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L.
Reiss, L.J. Holden, M. Georgiou: Slow Passage through
Bifurcation and Limit Points. Asymptotic Theory and
Applications.- M. Canalis-Durand: Formal Expansion of van
der Pol Equation Canard Solutions are Gevrey.- V. Gautheron,
E. Isambert: Finitely Differentiable Ducks and Finite
Expansions.- G. Wallet: Overstability in Arbitrary
Dimension.- F.Diener, M. Diener: Maximal Delay.- A.
Fruchard: Existence of Bifurcation Delay: the Discrete
Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the
Case of a Period-doubling Cascade.- E. Benoit: Linear
Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the
Local Study of Slow-fast Vector Fields: the Zoom.- S.N.
Samborski: Rivers from the Point ofView of the Qualitative
Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P.
van den Berg: Macroscopic Rivers

Zielgruppe

Research

Autoren/Hrsg.

Benoit, Eric

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Dynamic bifurcations.- Slow passage through bifurcation and limit points. Asymptotic theory and applications.- Formal expansion of van der pol equation canard solutions are gevrey.- Finitely differentiable ducks and finite expansions.- Overstability in arbitrary dimension.- Maximal delay.- Existence of bifurcation delay: The discrete case.- Noise effect on dynamic bifurcations: The case of a period-doubling cascade.- Linear dynamic bifurcation with noise.- A tool for the local study of slow-fast vector fields: The zoom.- Rivers from the point of view of the qualitative theory.- Asymptotic expansions of rivers.- Macroscopic rivers.