A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization

Chaotic and hyperchaotic systems with interesting behaviors have been of interest in the recent years. In this paper we introduce a hyperchaotic memristor oscillator which shows both stable and unstable fixed points. Such systems have been less investigated in the literatures. It should also to be noted that the proposed hyperchaotic system has only one nonlinearity which is a flux controlled memristor. Depending on the control parameter, the system displays different behaviors and coexisting attractors. A linear quadratic regulator based synchronization of the proposed hyperchaotic system is designed and numerically analyzed. We also design such a fuzzy based PID controller for chaos control in such a memristor oscillator.