Coexistence of attractors in a simple chaotic oscillator with fractional-order-memristor component: analysis, FPGA implementation, chaos control and synchronization

In this paper, the simplest chaotic oscillator with fractional-order-memristor component (SCOF) is proposed. Dynamical characteristics of the proposed chaotic oscillator are investigated both analytically and numerically. The results indicate that the proposed chaotic oscillator possesses novel dynamical characteristics: double-scroll chaotic attractor, four-scroll chaotic attractor and coexisting attractors. The proposed SCOF system is implemented in field programmable gate arrays (FPGA) using the Adomian decomposition method to verify the numerical simulation results. Finally, control and synchronization of the simple chaotic oscillator with fractional-order-memristor component is studied using the linear feedback control and the unidirectional linear error feedback coupling scheme, respectively.