Complex dynamics in a periodically perturbed electro-chemical system

Dynamical response of a passivation model subjected to parametric periodic and stochastic perturbations is studied numerically. In response to weak periodic modulation, the system exhibits a rich variety of resonance behavior and induced dynamics, including periodically induced oscillation, birhythmicity, switching between two bistable states, selection of one of the bistable states, mixed-mode and chaotic oscillations. These phenomena are discussed in terms of the stability of saddle focus and an incomplete homoclinic connection. Our numerical results are relevant for a wide class of electro-chemical oscillatory systems, where the re-injection of unstable trajectory on the neighborhood of a saddle focus is a typical feature in the phase space.