Continuous and differentiable approximation of a TaO memristor model for robust numerical simulations

Abstract

This paper proposes the introduction of appropriate continuous and differentiable approximations to discontinuous and piecewise differentiable functions respectively adopted in state equation and Ohm’s based law of the mathematical model of an extended memristor recently fabricated at Hewlett Packard labs. The study of this model is particularly timely because the material at the basis of the relative memristor device, i.e. Tantalum oxide, has been recently classified, together with Hafnium oxide, as one of the most plausible candidates for a large-scale manufacturing of memory resistive devices, especially for memory applications. However, recent studies have demonstrated that the adoption of discontinuous and/or piecewise differentiable functions in the differential algebraic equation set describing the complex dynamics of these devices may be the source of serious convergence issues in standard software packages. This calls for an impeding necessity to ameliorate mathematical descriptions of real memristors. In this paper we present a thorough study which aims at deriving the most appropriate set of continuous and differentiable approximants to the discontinuous and piecewise differentiable functions of the TaO memristor model.