Hybrid chaotic synchronisation between identical and non-identical fractional-order systems

Abstract

In this paper, a chaotic Hybrid Synchronisation (HS) for multiple Fractional-Order (FO) systems coupled with ring connection is proposed. For such schema, the Complete Synchronisation (CS) and the complete Anti-Synchronisation (AS) should coexist at the same time under designed control laws. It is clear that integer-order controllers are adept to synchronise asymptotically coupled FO systems. In order to prove the effectiveness of the synchronisation schema, two cases studies are considered where multiple identical FO systems and multiple non-identical FO systems are synchronised, respectively. Finally, numerical simulations illustrate the good resolution of the synchronisation problem under the designed control laws.