Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes

By using a remarkably simple and natural degenerate technique, the mechanism of chaos via torus breakdown observed in a simple four-dimensional autonomous circuit including two diodes is investigated rigorously. This degenerate technique is uniquely comparable to the well-known slow–fast singular perturbation method. The idealized case where the diodes are assumed to operate as switches is considered. In this case, the governing equation is represented by a constrained equation, and the Poincaré mapping is derived rigorously as the circle map. The torus breakdown in the four-dimensional autonomous circuit is well explained by the Poincaré mapping. The theoretical results are verified by laboratory experiment.