Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation

Abstract

The topic of discrete memristor has attracted more and more attention in recent years, but there is not enough discussion about discrete memristor under the fractional-order difference definition, especially for the system model defined by Grunwald–Letnikov. In this paper, a discrete fractional-order memristor model based on Grunwald–Letnikov definition is derived, and two new chaotic maps are designed based on this fractional-order model. Dynamic behaviors are investigated by the volt–ampere curve, bifurcation diagram, Lyapunov exponent spectrum, attractor phase diagram and fuzzy entropy complexity algorithm. Simulation results show that the two fractional-order systems can produce rich dynamic behaviors with the change of fractional order value, and both of them can present hyperchaos. Finally, the proposed systems are implemented in FPGA digital circuit and analog circuit respectively, and the phenomena in the numerical simulation are verified.