Characterizing the anticipating chaotic synchronization of RCL-shunted Josephson junctions

This study addresses the problem of anticipating synchronization of two chaotic RCL-shunted Josephson junctions (RCLSJ) based on time-delayed feedback control. The error dynamical system can be dealt with in virtue of non-linear pendulum-like system methods, through which we establish sufficient conditions to guarantee the existence of anticipating synchronizing slave systems. The design of a desired feedback controller can be achieved by solving a group of linear matrix inequalities (LMIs) by utilizing available numerical software. In the presence of parameter uncertainties, we further explore the robust anticipating synchronization, and propose corresponding criteria as well. These results are demonstrated through numerical simulations that under the derived conditions, the slave RCLSJ model could respond in exactly the same way as the master would do in the future, hence it allow us to anticipate the non-linear chaotic dynamics.