Chaos via torus breakdown in a piecewise-linear forced van der Pol oscillator with a diode

Chaos via torus breakdown in the piecewise-linear forced van de Pol equation is studied rigorously by using the degenerate technique. The model is a negative resistance LC oscillator including a diode driven by a sinusoidal voltage source. The authors investigate an idealized case where the diode is assumed to operate as an ideal switch. In this case, the Poincare map is derived strictly as a one-dimensional return mapping of a circuit onto itself. This mapping clarifies the onset of chaos via torus breakdown observed in this circuit. The authors obtain the critical value of the bifurcation parameter analytically, which gives the boundary between the chaotic region and the torus region. This bridges the gaps between the abstract one-dimensional mapping and the real circuit