Adaptive control and synchronization of a memristor-based Shinriki’s system

Abstract

The recent discovery of memristor has aroused great interest in the scientific community about this new fourth circuit element and its applications in spintronic devices, ultra-dense information storage, neuromorphic circuits and programmable electronics. Also, the intrinsic nonlinear characteristic of memristor has been exploited in implementing novel chaotic oscillators with complex dynamics, by replacing their nonlinear elements with memristors. However, the increased systems’ complexity, due to the use of memristor, have been raised significantly the interest for studying the cases of control of such systems as well as the synchronization of coupled memristive systems. So, to this direction, this chapter presents an adaptive controller, which is designed to stabilize a memristor-based chaotic system with unknown memristor’s parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of the memristor-based chaotic systems with unknown memristor’s parameters. The proposed chaotic system is a modified Shinriki nonlinear circuit, in which its nonlinear positive conductance has been replaced with a first order memristive diode bridge. All the main adaptive results in this chapter are proved using Lyapunov stability theory. The simulation results confirm the effectiveness of the proposed control and synchronization schemes.