Theory of heterogeneous circuits with stochastic memristive devices

TL;DR

This paper presents a novel analytical and numerical framework for modeling heterogeneous stochastic circuits that combine memristive devices with reactive components, enabling better understanding of complex stochastic networks.

Contribution

It introduces a Chapman-Kolmogorov equation-based approach to model circuits with stochastic memristive devices and reactive components, providing analytical solutions and a new modeling tool.

Findings

Analytical solutions for a binary memristor-capacitor circuit are derived.

The approach offers a versatile tool for modeling complex stochastic networks.

Potential applications span various fields involving stochastic circuit analysis.

Abstract

We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex stochastic networks, which may find a broad range of applications.