Control of chaos in discrete Josephson transmission lines

We have simulated the control of chaos by chaos in discrete Josephson transmission lines to obtain periodic outputs of selected frequency. Our system consists of an underdamped 1-D parallel array of 11 small Josephson junctions in the presence of an externally applied magnetic field. Control of chaos is achieved by a delayed feedback mechanism which selects one of the unstable periodic orbits embedded within the associated strange attractor. Although the dimensionality of our system is relatively large (22), control was achieved by applying the delayed feedback to a single boundary junction resulting in the above stable oscillatory output. The essence of our work shows that unwanted chaotic signals could be turned into useful applications such as microwave oscillators of variable frequency, without modifying the original system.