The Memory-Conservation Theory of Memristance

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 magneto statics 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.