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

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

2010-07-31

arxiv.org/abs/1008.0133v2

Mathematics

Dynamical Systems

13 pages, 6 figures. Accepted to the proceedings for the Eighth AIMS International Conference on Dynamical Systems, Differenti

Scientific paper

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.

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