Multiswitching compound–compound synchronisation of six chaotic systems

In this paper, a novel synchronisation scheme involving six chaotic systems is proposed. The proposed scheme is named as ‘compound–compound synchronisation’. Instead of using a scaling system in compound synchronisation, a compound scaling signal is applied to the proposed scheme. The phenomenon of multiswitching synchronisation and the proposed scheme are combined together. Appropriate controllers are designed by employing nonlinear control method and Lyapunov stability theory to achieve asymptotically stable synchronisation states. An example of identical Chen systems is presented to demonstrate the proposed methodology. The proposed scheme is very different and complex in comparison with the previous schemes, as this scheme is first of its kind having five drive systems and one response system. Computational results are presented to justify the theoretical analysis. Numerical results and theoretical studies converge to the same conclusions.