Multi-switching combination synchronization of three different chaotic systems via nonlinear control

In this paper, the multi-switching combination synchronization among three different chaotic systems is investigated. Multi-switching combination synchronization of chaotic systems means that the state variables of two drive systems synchronize with different state variables of one response system, simultaneously. Here, the Lorenz system and Chen system are considered as the drive systems, the combination of the multi-drive systems is synchronized with Lü response system using multi-switching synchronization method. Based on nonlinear control technique and Lyapunov stability theory, sufficient conditions are obtained to achieve the desired synchronization among three different chaotic systems. For suitable choice of scaling factors, switching modified projective synchronization is obtained as a special case of multi-switching combination synchronization among different chaotic systems. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed scheme.