Detectable canard cycles with singular slow dynamics of any order at the turning point (Q628760)

Limit cycles that appear in planar slow-fast systems are studied from the viewpoint of geometric singular perturbation theory. The main focus is on the limit cycles of FSTS-type, i.e., closed orbits, composed of a fast branch, an attracting slow branch, a turning point, and a repelling slow branch. Techniques to bound the number of limit cycles near an FSTS-l.p.s. are based on the study of the slow divergence integral calculated along the slow branches. In this paper, these techniques are extended to the case when the slow divergence integral becomes unbounded, that is, the slow dynamics has singularities of any finite order that accumulate to the turning point. By using the derivatives of the slow divergence integral, the number of limit cycles near the FSTS-l.p.s. are estimated.