Discretized Fast-Slow Systems with Canard Points in Two Dimensions
We study the behaviour of slow manifolds for two different discretization
schemes of fast-slow systems with canard fold points. The analysis uses the
blow-up method to deal with the loss of normal hyperbolicity at the canard
point. While the Euler method does not preserve the folded canard, we can show
that the Kahan discretization allows for a similar result as in continuous
time, guaranteeing the occurence of canard connections between attracting and
repelling slow manifolds upon variation of a bifurcation parameter.
Furthermore, we investigate the existence and properties of a formal conserved
quantity in the rescaled Kahan map.