Numerical computation of canards

Singularly perturbed systems of ordinary differential equations arise in ma ny biological, physical and chemical systems. We present an example of a si ngularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically co mputed using continuation of solutions of boundary value problems. One of t hese periodic orbits contains canards, trajectory segments that follow unst able portions of a slow manifold. We identify several mechanisms that lead to the formation of these and other canards in this example.