FULL AND REDUCED-ORDER SYNCHRONIZATION OF CHAOS IN JOSEPHSON JUNCTION

In this paper, the synchronization between two diff erent Josephson junction models is investigated bas ed on variable back-stepping technique. Firstly, we examined the s ynchronization of identical RCL-shunted Josephson junction (RCLSJ) systems emanating from different initial conditions by means of a proposed variable back-stepping tech nique. Secondly, by utilizing a reduced-order synchronization technique , we realized synchronization between the third ord er RCLSJ model and the parametrically modulated Josephson junction (PMJJ) system (second order). In both cases, the desi gned controllers are singular in nature and thus easier to construct and implement in practice. They ensure that the state s of the controlled chaotic slave system exponentially synchronize with the sta te of the master system. Numerical simulations are illustrated to verify the proposed methods.