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We consider double canard cycles including two canards in singularlyperturbed planar systems with two canard points. Previous work studied thecomplex oscillations including relaxation oscillations and canard cycles insingularly perturbed planar systems with one-parameter layer equations, whichhave precisely one canard point, two jump points or one canard point and onejump point. Based on the normal form theory, blow-up technique and Melnikovtheory, we investigate double canard cycles induced by two Hopf breakingmechanisms at two non-degenerate canard points. Finally, we apply the obtainedresults to a class of cubic Lienard equations with quadratic damping.

Double canard cycles in singularly perturbed planar systems with two canard points