OPF chaos control in a circuit containing a feedback voltage pulse generator

In this paper, we discuss occasional proportional feedback (OPF) chaos control in a circuit containing a feedback voltage pulse generator. First, we show that the Poincare map of this oscillator without the chaos control is derived rigorously as a one-dimensional mapping. This mapping satisfies Li-Yorke's extended period three condition (1975). Hence, the mapping has an n-periodic point for any natural number n, and the appearance of chaos in Li-Yorke's sense is explained. Furthermore, OPF for piecewise-linear systems is applied to this oscillator. Each unstable orbit can be stabilized, and periodic orbits with one to ten periods are successfully stabilized in circuit experiments.