Fixed-Time Multi-Switch Combined–Combined Synchronization of Fractional-Order Chaotic Systems with Uncertainties and External Disturbances

Abstract

In this paper, the fixed-time multi-switch combination–combination synchronization (FTMSCCS) of fractional-order chaotic systems with uncertainties and external disturbances is studied. The appropriate sliding mode surface and controller are proposed based on a Lyapunov theorem, and fixed-time multi-switching combination–combination synchronizations between four fractional-order chaotic systems are realized. The Lyapunov function is designed to prove the feasibility of the controller theoretically, and the effectiveness and robustness of the synchronization mechanism are further verified by numerical simulations. The advantage of this article is that it extends fixed-time synchronization to multi-switch combination–combination synchronization, enabling synchronization for a limited time, while increasing the complexity of the synchronization mechanism and improving its confidentiality in communication applications.