Dual Combination Synchronization of the Fractional Order Complex Chaotic Systems

Abstract

In this article, the authors have proposed a novel scheme for the dual combination synchronization among four master systems and two slave systems for the fractional order complex chaotic systems. Dual combination synchronization for the integer order has already been investigated in real space; but for the case of fractional order in complex space, it is the first of its kind. Due to complexity and presence of additional variable, it will be more secure and interesting to transmit and receive signals in communication theory. Based on the Lyapunov stability theory, six complex chaotic systems are considered and corresponding controllers are designed to achieve synchronization. The special cases, such as combination synchronization, projective synchronization, complete synchronization, and many more, can be derived from the proposed scheme. The corresponding theoretical analysis and numerical simulations are shown to verify the feasibility and effectiveness of the proposed dual combination synchronization scheme.