Canard solutions of two-dimensional singularly perturbed systems

In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an th-order degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing results. Finally, one numerical example is given.