Canard Cycles and Center Manifolds

Canard Cycles and Center Manifolds
Author :
Publisher : American Mathematical Soc.
Total Pages : 117
Release :
ISBN-10 : 9780821804438
ISBN-13 : 082180443X
Rating : 4/5 (38 Downloads)

Book Synopsis Canard Cycles and Center Manifolds by : Freddy Dumortier

Download or read book Canard Cycles and Center Manifolds written by Freddy Dumortier and published by American Mathematical Soc.. This book was released on 1996 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.


Canard Cycles and Center Manifolds Related Books

Canard Cycles and Center Manifolds
Language: en
Pages: 117
Authors: Freddy Dumortier
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon
Canard Cycles
Language: en
Pages: 408
Authors: Peter De Maesschalck
Categories: Mathematics
Type: BOOK - Published: 2021-08-07 - Publisher: Springer Nature

DOWNLOAD EBOOK

This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are
Structured Population Models in Biology and Epidemiology
Language: en
Pages: 314
Authors: Pierre Magal
Categories: Mathematics
Type: BOOK - Published: 2008-04-12 - Publisher: Springer

DOWNLOAD EBOOK

In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new disea
Singular Perturbations
Language: en
Pages: 224
Authors: Elena Shchepakina
Categories: Mathematics
Type: BOOK - Published: 2014-10-06 - Publisher: Springer

DOWNLOAD EBOOK

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples a
Equadiff 99 (In 2 Volumes) - Proceedings Of The International Conference On Differential Equations
Language: en
Pages: 838
Authors: Bernold Fiedler
Categories: Mathematics
Type: BOOK - Published: 2000-09-05 - Publisher: World Scientific

DOWNLOAD EBOOK

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical sys