A pendulum-like system approach to the anticipating synchronization of RCL-shunted Josephson junctions

In virtue of the nonlinear pendulum-like system theory, this study addresses the problem of anticipating synchronization of two coupled chaotic RCL-shunted Josephson junctions (RCLSJ) based on time-delayed feedback control. Sufficient conditions are established, under which the existence of anticipating synchronizing slave systems is guaranteed. The design of a desired feedback controller can be achieved by solving a group of linear matrix inequalities by utilizing an available numerical software. In the presence of parameter uncertainties, robust anticipating synchronization is further explored. 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 allows us to anticipate the nonlinear chaotic dynamics.