Fractional-order cubic nonlinear flux-controlled memristor: theoretical analysis, numerical calculation and circuit simulation

Abstract

Many studies have proved that the fractional-order system is more accurate than the integer-order system. The theory of fractional calculus has received extensive attention in many fields. The research on flux-controlled memristor has been carried out for several years; however, fractional-order flux-controlled memristor has not received widespread attention. In light of the theory of fractional calculus, a generalized fractional-order dynamic model of flux-controlled memristor is proposed for the first time in this paper. The mathematical model is established and its characteristics of the pinched hysteresis loops are analyzed by changing the order and the frequency. The specific computational formulas of areas of pinched hysteresis loops are given. The equivalent circuit of the fractional-order flux-controlled memristor is constructed, and circuit simulations are given to illustrate the effectiveness of theoretical analysis and numerical calculation. In this study, the flux-controlled memristor model is extended to the fractional-order model that is closer to the real device, and the analysis method of areas of pinched hysteresis loops is further expanded.