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Journal of Dynamical and Control Systems

, Volume 16, Issue 2, pp 267–300 | Cite as

Ducks on the torus: existence and uniqueness

  • I. V. Schurov
Article

Abstract

We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have 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. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.

Key words

and phrases Slow-fast systems canards limit cycles Poincaré map distortion lemma 

2000 Mathematics Subject Classification

34E15 37G15 70K70 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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