Takacs Model of Hysteresis in Mathematical Modeling of Memristors

Abstract

In this paper, the mathematical modeling of memristor via Takacs model of hysteresis is presented along with a modification of this model tailored to describe the asymmetric hysteresis loop and first order reversal curves. In particular, it is shown that there is a class of differential equations of the Duhem model of hysteresis where every member of the class could play a role of the state equation of memristor. Within this class of Duhem differential equations, there are two distinct subclasses: one corresponding to the Takacs model and the other one corresponding to the state equations of the memristor model with the Biolek window function of various degrees p. These two subclasses have a non-empty intersection, which contains the state equation of the memristor model with the Biolek window function for p = 1. To demonstrate the proposed approach, three examples are presented.

Effect of SiO2 sublayer on the retention characteristics of nanometer-sized Si3N4 memristive devices investigated by low-frequency noise spectroscopy

“…Today's understanding of the bipolar RS mechanism in oxides is based on the concept of conductive filaments consisting of the oxygen vacancies, formed inside the dielectric films along the electric field lines between conductive electrodes. [26][27][28][29][30] In the low resistance state (LRS) of the memristor, the filaments shortcut the electrodes of the memristor structure. Switching to the high resistance state (HRS) is achieved by applying a reverse voltage to the electrodes leading to the rapture of the filaments.…”