Mathematical model of memristor with sensory memory

Abstract

In Atkinson-Shiffrin model, the formation of human memory includes three stages:sensory memory (SM), short-term memory (STM), and long-term memory (LTM). A similar memory formation process has been observed and reported in the experimental studies of memristors fabricated by different materials. In these reported experiments, the increase and decrease of the memristance (resistance of a memristor) would normally be regarded as the loss and formation of the memory of the device. These memristors can be divided into two types based on the memory formation process. The memory formation of some memristors consists of only STM and LTM, and these memristors in this paper are called STM → LTM memristors; the memory formation of other memristors contains all three stages like human memory, and these memristors here are named SM → STM → LTM memristors. The existing mathematical model of this kind of memristor can only describe the STM → LTM memristor. Three state variables are included in this model:w describes the memory of the device, <i>w</i>_min describes the long-term memory, and <i>τ</i>_<i>w</i>0 is the time constant of the forgetting curve of the short-term memory. In this paper, a phenomenological memristor model is proposed for SM → STM → LTM memristors. The model is designed by redefining <i>a</i>₊, a constant in the existing STM → LTM memristor model, as a state variable, and the design of corresponding state equation is based on the reported experimentally observed behaviors of SM → STM → LTM memristors during the SM period. Simulations of the proposed model show its ability to describe the behavior of SM → STM → LTM memristors. Stimulated by repeated positive pulses starting from the high-memristance state, the memristor stays in the SM state during the stimulation of first several pulses, and no obvious memory is formed during this period; STM and LTM would be gradually formed when the following pulses are applied. A faster memory formation speed can be achieved by applying pulses with longer duration, shorter interval, or higher amplitude. The formation and annihilation of the conductive channel between two electrodes of a memristor is a commonly used explanation for the change of the memristance. In this model, w can be understood as the normalized area index of the conductive channel, <i>w</i>_min is the normalized area index of the stable part of the conductive channel, <i>τ</i>_<i>w</i>0 describes the amount of time taken by the annihilation of the unstable part, and <i>a</i>₊ determines the variation of the conductive channel when different positive voltages are applied.