Special Fractional-Order Map and Its Realization

Abstract

Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with “hidden attractors”. The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system’s parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting.

Keywords

• fractional map
• chaos
• discrete memristor
• initial-boosting attractors