Alpha-stable based stochastic GMMS memristor model

This is an implementation that incorporates the variability of the hysteresis cycles within the Generalized Mean Metastable Switch Memristor Model (GMMS) based on the empirical alpha-stable characterization for the probability distributions of the Set and Reset thresholds of a typical Knowm SDC memristor.

To produce sequences of values with the distributions of interest, namely alpha-stable and Gaussian distributions, incorporating these within the GMMS model to introduce the desired variability at the V_OFF and V_ON thresholds, in a simple and efficient way (with less computational time consumption although at the cost of requiring some reserved memory space), Monte Carlo roulette principle was employed, using tables of 1000 records and an index that determines the retrieved value by means of a uniform distribution. In all cases, the tables must store predetermined values, which correspond to an ordered sequence of samples and whose empirical distribution profile corresponds precisely to the desired random variable.

Demo code: Execute the python main code stochastic_GMMS_memristor_demo.py.

Demo code: Execute the python main code alpha-stable_demo.py.

The prposed model can be considered as acceptable approximations for simulation purposes, especially, taking into account that the variation in behavior between memristors of the same type, even within the same package, is notorious and significant. In such circumstances, it makes no practical sense to maximize the accuracy of approximations during the characterization of any random variable under study and, much less, to expect a simulation to faithfully reproduce the distribution profile of a certain reference random variable. It is sufficient for all this to be done in an approximate manner.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Fork the code to make the model more complicated, detailed, or accurate.

The published work that complements the code of this repository is the following:

• Laguna-Sanchez, G. A., Lopez-Guerrero, M., & Barron-Fernandez, R. (2023). The probabilistic behavior of the set and reset thresholds in Knowm’s SDC memristors: Characterization and Simulation. IEEE Latin America Transactions, 21(12), 1266–1274. Retrieved from https://latamt.ieeer9.org/index.php/transactions/article/view/8308

This paper outlines, in more detail, the related work and formal background of this proposal.

• Generalized Mean Metastable Switch Memristor Model (GMMS)

• T. Molter and A. Nugent, “The Mean Metastable Switch Memristor Model in Xyce,” Knowm web page, 2017. https://knowm.org/the-mean-metastable-switch-memristor-model-in-xyce/

Specifically, to write this code, I took as a starting point the GMMS model improved in:

• V. Ostrovskii, P. Fedoseev, Y. Bobrova, and D. Butusov, “Structural and Parametric Identification of Knowm Memristors,” Nanomaterials, Vol.12. No. 63, pp. 1–20, 2022. https://doi.org/10.3390/nano12010063

If you mention this model in a publication, I ask that you include these citations for the model:

• Laguna-Sanchez, G.A. (2022). Alpha-stable based stochastic GMMS memristor model. https://github.com/galaguna/Stochastic_GMMS_memristor_model.

Copyright 2022 Gerardo Abel Laguna-Sanchez.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or(at your option) any later version. See http://www.gnu.org/licenses/