Compound-Combination Synchronization for Fractional Hyperchaotic Models with Different Orders

Abstract

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described and proved. We introduce, also, the FO hyperchaotic complex Lü, Chen, and Lorenz models with complex periodic forcing. The symmetry property is found in the FO hyperchaotic complex Lü, Chen, and Lorenz models. These hyperchaotic models are found in many areas of applied sciences, such as physics and secure communication. These FO hyperchaotic models are used as an example for our proposed synchronization. The numerical simulations show a good agreement with the analytical results. The complexity and existence of additional variables mean that it is safer and interesting to transmit and receive signals in communication theory. The proposed scheme of synchronization is considered a generalization of many types in the literature and other examples can be found in similar studies.