Adaptive anti-synchronization of 5-D novel hyperchaotic systems and SPICE implementation

Chaos theory has wide applications and its importance can be seen by voluminous publications giving these applications in several branches of science, commerce and engineering. As application problems, control, tracking or regulation and synchronization of different types are important areas of research in the control literature and various methods have been adopted over the past few decades for tackling these research problems. Also, the discovery of novel chaotic systems in various applications, their qualitative properties and the control of such systems are also important research areas in chaos theory. This special paper proposes a novel 5-D hyperchaotic system and details its qualitative properties such as Lyapunov exponents and Lyapunov dimension. Next, the main result of this paper, namely, an adaptive feedback controller has been constructed for the drive-response anti-synchronization of novel 5-D hyperchaotic systems for all initial states when the system parameters are unknown. Anti-phase synchronization of hyperchaotic systems is characterized by vanishing of sums of the respective variables. Finally, for the 5-D hyperchaotic system, an electronic circuit realization in SPICE has been described in detail to confirm the feasibility of the theoretical model.