Generalized compound synchronization of chaos in different orders chaotic Josephson junctions

Abstract

This paper investigates compound synchronization scheme between three drive Josephson junctions and one response Josephson junction of a different order via the active backstepping technique. Reduced-order projective compound synchronization and anti-synchronization as well as reduced order hybrid projective synchronization between three third order Josephson junctions and one second order Josephson junction are considered. In each case, sufficient conditions for global asymptotic stability for generalized compound synchronization of different Josephson junctions are achieved via the active backstepping technique. Numerical simulations are performed to validate the effectiveness of the proposed synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.