Canard Cycles and Center Manifolds (Memoirs of the American Mathematical Society)

By Freddy Dumortier

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.

• Format: Paperback
• Language: English
• ISBN: 082180443X
• ISBN13: 9780821804438
• Release Date: January 1996
• Publisher: Amer Mathematical Society
• Length: 96 Pages
• Weight: 0.55 lbs.
• Dimensions: 10.3" x 0.3" x 7.3"