Chaos via torus breakdown in the forced van der Pol oscillator

Chaos in the forced van der Pol oscillator including a pair of diodes is investigated. First, the authors show that the normal forced van der Pol equation exhibits chaos. The generation of chaos is explained by a Lorenz plot. Secondly, they analyze chaos rigorously by using a piecewise-linear technique and a degeneration technique which corresponds to an idealized case where the diode is assumed to operate as an ideal switch. In this case, the Poincare map is derived strictly as one-dimensional mapping which is a noninvertible return mapping of a circle. This mapping clarifies the mechanism of chaos.<
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