Memristive Networks: from Graph Theory to Statistical Physics

TL;DR

This paper introduces a toy model of memristive networks, analyzing how circuit topology influences dynamics and connecting asymptotic states to the Ising model and disordered systems.

Contribution

It provides an exact differential equation for memristive network dynamics incorporating Kirchhoff laws and explores the relationship with graph theory and statistical physics.

Findings

Exact differential equation for memristor dynamics

Connection between network states and the Ising model

Analysis of topology's role in memristive behavior

Abstract

We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.