Dynamic Bifurcations

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