Full and Reduced-order Synchronization of Chaos in Josephson Junction

Abstract

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