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CANARD CYCLES IN GENERIC FAST-SLOW SYSTEMS ON THE TORUS

By I. V. Shchurov

Abstract

Abstract. In generic fast-slow systems with a single parameter on the two-dimensional torus, for arbitrarily small values of this parameter there exist attracting canard cycles. This is a key distinction between the dynamicsonthetorusandthedynamics of similar systems on the plane. This has already been proved for systems with a convex slow curve. This paper looks at systems with a nonconvex slow curve. Upper and lower estimates for the number of canard cycles are obtained. An open set of systems having a preassigned number of attracting canard cycles is constructed. 1

Topics: 1.1
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.6739
Provided by: CiteSeerX
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