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 local dynamics lying on S-shaped critical manifolds, we give a sufficient condition under which there exist three hyperbolic limit bifurcating from some cycles. The proof is based geometric singular perturbation theory. Then, apply results to cubic Liénard equations quadratic damping, and prove coexistence large enclosing equilibria. This new dynamical configuration has never been previously found existing references.