Abstract
In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3-D master chaotic system and 4-D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein.