Torus Breakdown and Homoclinic Chaos in a Glow Discharge Tube

Starting from historical researches, we used, like Van der Pol and Le Corbeiller, a cubic function for modeling the current–voltage characteristic of a direct current low-pressure plasma discharge tube, i.e. a neon tube. This led us to propose a new four-dimensional autonomous dynamical system allowing to describe the experimentally observed phenomenon. Then, mathematical analysis and detailed numerical investigations of such a fourth-order torus circuit enabled to highlight bifurcation routes from torus breakdown to homoclinic chaos following the Newhouse–Ruelle–Takens scenario.