Chaos Synchronization of Directionally Coupled and Periodically Modulated Josephson Junctions and its Application to Secure Communications

In this paper, we investigate global chaos synchronization of unidirectionally coupled and periodically modulated Josephson junctions (PMJJs) based on the stability theory of linear time-varied systems and Lyapunov's direct method. Some necessary and sufficient criteria for global asymptotic stability are derived from which an estimate of the threshold coupling for the on-set of complete synchronization is obtained. The analytical and numerical results reveal that the synchronization criteria based on Lyapunov's direct method are sharper than the criteria based on the stability theory of linear time-varied systems. Based on the criteria obtained via Lyapunov direct method, we showed that the method can be applied to secure communication. The numerical simulations results presented verify the effectiveness of theoretical analysis and the proposed scheme's success in secure communication.