Double canard cycles in singularly perturbed planar systems

We study the bifurcations of slow-fast cycles with two canard points in singularly perturbed planar systems. After analyzing the local dynamics of two canard points lying on the S-shaped critical manifolds, we give a sufficient condition under which there exist three hyperbolic limit cycles bifurcating from some slow-fast cycles. The proof is based on the geometric singular perturbation theory. Then, we apply the results to cubic Liénard equations with quadratic damping, and prove the coexistence of three large limit cycles enclosing three equilibria. This is a new dynamical configuration and has never been previously found in the existing references.