Asymptotic expansions for a degenerate canard explosion (Q2077863)

The problem of a turning point (including degenerate turning point) is a key issue in singular perturbation theory. This article develops a new way, namely, the asymptotic expansion approach of suitable order, to detect canard explosion generated by the higher-order (degenerate) turning point in a two-dimensional singularly perturbated system. By this method, the canard curve can also be calculated with respect to the perturbation parameter to arbitrary order. It is shown that this asymptotic expansion-based method is quite effective to analyze the canard explosion phenomena generated by the degenerate turning point.