Takacs Model of Hysteresis in Mathematical Modeling of Memristors

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.