Analytical studies on complete, lag and anticipation synchronization in cascaded circuits with numerical and experimental confirmation

Abstract

We report in this paper, the explicit analytical solutions developed for studying the different types of synchronization behaviors such as complete, lag and anticipation synchronization observed in cascaded circuits without any delay factors in the system. The Pecora–Carroll method of synchronization of unidirectionally coupled systems, which has not been earlier studied through explicit analytical solutions is reported in this paper. The emergence of different synchronization phenomena and the nature of evolution of the synchronization behavior has been discussed. Further, it has also been confirmed that the evolution of anticipation from lag through complete synchronization along with the attenuation, amplification of the subsystem signal occurs as a generalized phenomenon irrespective of the nature of the chaotic attractor state of the drive and the system parameters. The Hamilton energy of the cascaded system for different types of synchronization is reported. The numerical simulation and electronic circuit experimental results are presented to confirm the analytical results.