New hybrid synchronisation schemes based on coexistence of various types of synchronisation between master-slave hyperchaotic systems

Abstract

In this paper, we present new approaches to study the co-existence of some types of synchronisation between hyperchaotic dynamical systems. The paper first analyses, based on stability theory of linear continuous-time systems, the co-existence of the projective synchronisation (PS), the function projective synchronisation (FPS), the full state hybrid function projective synchronisation (FSHFPS) and the generalised synchronisation (GS) between general master and slave hyperchaotic systems. Successively, using Lyapunov stability theory, the co-existence of three different synchronisation types is proved, i.e., the inverse projective synchronisation (IPS), the inverse function projective synchronisation (IFPS), the inverse full state hybrid function projective synchronisation (IFSHFPS) and the inverse generalised synchronisation (IGS) are proved to co-exist between arbitrary master and slave systems. Finally, several numerical simulations of co-existence of synchronisation types are illustrated, with the aim to show the effectiveness of the approaches developed herein.