Controlling chaos in a chaotic circuit controlled by voltage pulse

In this paper, we discuss controlling chaos in a chaotic circuit. Our circuit is a negative resistance LC oscillator whose amplitude is controlled by DC voltage pulses. First, we show that the Poincare map of this oscillator is derived rigorously as a one-dimensional mapping. This mapping satisfies Li-Yorke´s extended period three condition. Hence, the mapping has a n-periodic point for any natural number n, and the appearance of chaos in Li-Yorke´s sense is explained. Furthermore, an occasional proportional feedback method (OPF method) for piecewise-linear systems is applied to this oscillator. Each unstable orbit can be stabilized, and periodic orbits with one to ten period are successfully stabilized in circuit experiments