Duck farming on the two-torus: Multiple canard cycles in generic slow-fast systems

Pages: 1289 - 1298, Issue Special, September 2011

 Abstract        Full Text (222.1K)              

Ilya Schurov - Higher School of Economics — National Research University, Room 518, 3, Kochnovsky pr-d, Moscow, Russian Federation (email)

Abstract: Generic slow-fast systems with only one (time-scaling) parameter on the two-torus have attracting canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. In present work, general case of nonconvex slow curve with several fold points is considered. The number of canard cycles in such systems can be effectively computed and is no more than the number of fold points. This estimate is sharp for every system from some explicitly constructed open set.

Keywords:  Slow-fast systems, canards, limit cycles, PoincarĂ© map, equation of variations
Mathematics Subject Classification:  Primary: 34E15, 37G15

Received: July 2010;      Revised: April 2011;      Published: October 2011.