Ducks on the torus: existence and uniqueness - Mathematics > Dynamical SystemsReport as inadecuate




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Abstract: We show that there exist generic slow-fast systems with only onetime-scaling parameter on the two-torus, which have canard cycles forarbitrary small values of this parameter. This is in drastic contrast with theplanar case, where canards usually occur in two-parametric families. Here wetreat systems with a convex slow curve. In this case there is a set ofparameter values accumulating to zero for which the system has exactly oneattracting and one repelling canard cycle. The basin of the attracting cycle isalmost the whole torus.



Author: Ilya Schurov

Source: https://arxiv.org/







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