Canard trajectories in 3D piecewise linear systems

Abstract

We present some results on singularly perturbed piecewise linear systems, similar to those obtained by the Geometric Singular Perturbation Theory. Unlike the differentiable case, in the piecewise linear case we obtain the global expression of the slow manifold ${\mathcal S}_{\varepsilon}$. As a result, we characterize the existence of canard orbits in such systems. Finally, we apply the above theory to a specific case where we show numerical evidences of the existence of a canard cycle.