A systematic study of two-dimensional 2-layer canard cycles

Abstract The paper deals with two-dimensional 2-layer canard cycles, extending the results of Dumortier and Roussarie (2007 Discrete Contin. Dyn. Syst. 17 787–806) and continuing the approach started in De Maesschalck et al (2023 Regul. Chaotic Dyn. 28 763–80). We provide precise results on the number and the bifurcations of the limit cycles that can be created from the canard cycles, confirming that both the type of the layers and the nature of the connections between the layers make a difference. We also prove an upper bound on the cyclicity of a large class of two-dimensional 2-layer canard cycles.