Synchronization of Three-Scroll Unified Chaotic System (TSUCS) and its hyper-chaotic system using active pinning control

This paper studies the synchronization and anti-synchronization problem of the Three-Scroll Unified Chaotic System (TSUCS), which has nonlinear terms in each subsystem. By virtue of active control, a novel active pinning control strategy is presented, which only needs one or two states of the TSUCS. Under the proposed controller, the synchronization of two TSUCS with parametric uncertainty is achieved and therefore the robust stability of TSUCS synchronization is ensured. Some stability theories about synchronization and anti-synchronization have been given and proved the use of this class of a novel TSUCS and its hyper-unified chaotic system with the active pinning control strategy. Numerical simulations are given to verify the theoretical analysis, which clearly shows that the control strategy can really make the chaotic systems achieve synchronization and anti-synchronization in a quite short time.