Window functions and sigmoidal behaviour of memristive systems

TL;DR

This paper establishes a theoretical link between window functions and sigmoidal curves in memristive systems, enabling data-driven modeling and introducing a flexible new window function for asymmetric effects.

Contribution

It demonstrates that window functions can be derived from sigmoidal curves and introduces a new generalized window function for asymmetric edge effects in memristive systems.

Findings

Each window function relates to a sigmoidal curve of normalized memristance

Sigmoidal curves can be extracted from device input-output signals

A new generalized window function models asymmetric edge effects

Abstract

A common approach to model memristive systems is to include empirical window functions to describe edge effects and non-linearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner.