具有感觉记忆的忆阻器模型

Mathematical model of memristor with sensory memory

人类记忆的形成包括感觉记忆、短期记忆、长期记忆三个阶段,类似的记忆形成过程在不同材料忆阻器的实验研究中有过多次报道.这类忆阻器的记忆形成过程存在有、无感觉记忆的两种情况,已报道的这类忆阻器的数学模型仅能够描述无感觉记忆的忆阻器.本文在已有模型的基础上,根据有感觉记忆的忆阻器的研究文献中所报道的实验现象,设计了具有感觉记忆的忆阻器模型.对所设计模型的仿真分析验证了该模型对于存在感觉记忆的这类忆阻器特性的描述能力:对忆阻器施加连续脉冲激励,在初始若干脉冲作用时忆阻器无明显的记忆形成,此时忆阻器处于感觉记忆阶段,后续的脉冲作用下忆阻器将逐渐形成短期、长期记忆,并且所施加脉冲的幅值越大、宽度越大、间隔越小,则感觉记忆阶段所经历的脉冲数量越少.模型状态变量的物理意义可用连通两电极的导电通道在外加电压作用下的形成与消失来给出解释.

In Atkinson-Shiffrin model, the formation of human memory includes three stages: sensory memory(SM), shortterm 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, wmin describes the long-term memory, and τ_w0 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 a_+, 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, wmin is the normalized area index of the stable part of the conductive channel, τ_w0 describes the amount of time taken by the annihilation of the unstable part, and a_+determines the variation of the conductive channel when different positive voltages are applied.