Canard cycles in generic fast-slow systems on the torus


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 dynamics on the torus and the dynamics 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.

Transactions of the Moscow Mathematical Society, 2010, 175–207