The Memory-Conservation Theory of Memristance

Abstract

The memristor, the recently discovered fundamental circuit element, is of great interest for neuromorphic computing, nonlinear electronics and computer memory. It is usually modelled either using Chua's equations, which lack material device properties, or using Strukov's phenomenological model (or models derived from it), which deviates from Chua's definitions due to the lack of a magnetic flux term. It is shown that by modelling the magnetostatics of the memory-holding ionic current (oxygen vacancies in the Strukov memristor), the memristor's magnetic flux can be identified as the flux arising from the ions. This leads to a novel theory of memristance consisting of two components: 1. A memory function which describes how the memristance, as felt by the ions, affects the conducting electrons located in the 'on' part of the device; 2. A conservation function which describes the time-varying resistance in the 'off' part of the device. This model allows for a straight-forward incorporation of the ions within the electronic theory and relates Chua's constitutive definition of a memristor with device material properties for the first time.

The bipolar and unipolar reversible behavior on the forgetting memristor model

“…There are many window functions [22], [28], here just list three of them, the ones proposed by Joglekar et.al (the J for short) [37], Biolek et.al (the B for short) [15], and Chang et.al (the C for short) [21]:…”

“…A detail comparison between this model and the popular memristor models (The HP [15], the Gale [37], the Simmons [17], the TEAM [22], the compact [24], the Chang [21], the threshold [30], the PWL (piecewise linear) [31], the appropriate [32], the Zhang [23], the Li [16], the Fang [26], the Kim [25]), and the thermophoresis [18] is taken in Table II. We can find that the model as a 3D dynamical system gets a special advantage on describing various memristors with an average number of parameters.…”

Non-ideal memristors for a non-ideal world

“…The total current, I is a sum of the electronic current, i e and ionic current, i v : …”

“…Thus, for step t , we can write where the vertical bar means the expression is evaluated at that external time, that is, would be the current due only to the decay of the short‐term memory as expected at time t after stimulation. The simulation we do is where i e is calculated from the memory‐conservation theory and we have taken the assumption that I ( t ) is only due to i e (an assumption of ‘vanilla’ mem‐con theory ). Essentially, we have two decays happening with different timescales; the second term adds a second charge carrier which is lagging the electronic current more slowly.…”

Spiking in Memristor Networks

“…The memory-conservation model of memristance [18] is a recently announced theoretical model that relates real world q and ϕ to Chua's constitutive equations and has been successful in modeling our memristors [19]. The memory-conservation theory has the concept of a memory property, the physical or chemical attribute of the device that holds the memory of the device.…”