A phenomenological memristor model for short-term/long-term memory

Memristor is considered to be a natural electrical synapse because of its distinct memory property and nanoscale. In recent years, more and more similar behaviors are observed between memristors and biological synapse, e.g., short-term memory (STM) and long-term memory (LTM). The traditional mathematical models are unable to capture the new emerging behaviors. In this article, an updated phenomenological model based on the model of the Hewlett–Packard (HP) Labs has been proposed to capture such new behaviors. The new dynamical memristor model with an improved ion diffusion term can emulate the synapse behavior with forgetting effect, and exhibit the transformation between the STM and the LTM. Further, this model can be used in building new type of neural networks with forgetting ability like biological systems, and it is verified by our experiment with Hopfield neural network.     

A mathematical analysis: From memristor to fracmemristor

The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO₂ memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements.     

具有感觉记忆的忆阻器模型

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.     

一种改进的WOx忆阻器模型及其突触特性分析

忆阻器被定义为第四种基本电子元器件, 其模型的研究呈现多样性. 目前, 忆阻器模型与忆阻器实际特性的切合程度引起了研究者的广泛关注. 通过改变离子扩散项, 提出了一种新的WO_x忆阻器模型, 更好地匹配了忆阻器的实际行为特性. 首先, 新的模型不仅能够描述忆阻器的一般特性, 而且能够俘获记忆丢失行为. 另外, 将新的忆阻器作为神经突触, 分析了脉冲速率依赖可塑性、短期可塑性、长期可塑性, 并发现了与生物系统中极为相似的“经验学习”现象. 最后, 考虑到温度与离子扩散系数的关系, 探讨了温度对突触权值弛豫过程的影响. 实验表明, 新忆阻器模型比原来的模型更切合实际, 且更适合作为突触而应用到神经形态系统之中.     

具有突触特性忆阻模型的改进与模型经验学习特性机理

许多忆阻器都具有与生物神经突触功能相似的特性,这些特性包括记忆与遗忘特性、经验学习特性等.文献[17]根据记忆与遗忘特性建立了这类忆阻器的模型,文献[19,20]在对该模型的仿真研究中发现该模型也具有描述经验学习特性的能力.在关于这一模型已有研究的基础上,本文对该模型状态方程的特性与机理给出进一步的分析.分析中发现原模型的窗口函数的设计和使用存在问题,并且原模型建模时对于实验现象的解读不够准确.针对这些问题对原模型的状态方程进行了改进,完善了模型功能.对于该模型能够描述经验学习特性的机理,分别利用对于模型的状态方程的分析以及周期脉冲信号作用下的状态方程解析分析,对该机理给出定性和定量的讨论.利用机理分析所得的相关结论,设计了基于经验学习实验的模型状态方程中的参数和函数的估计方法,方便了该模型在这一类忆阻器的实验研究中的应用.     

一个分数阶忆阻器模型及其简单串联电路的特性

忆阻器是具有时间记忆特性的非线性电阻. 经典HP TiO₂忆阻器模型的忆阻值为此前通过忆阻器电流的时间积分, 即记忆没有损失. 而最近研究证实HP TiO₂ 线性忆阻器掺杂层厚度不能等于零或者器件整体厚度, 导致器件的记忆有损失. 基于此发现, 本文首先提出了一个阶数介于0 与1间的分数阶HP TiO₂ 线性忆阻器模型, 研究了当受到周期外激励时, 分数阶导数的阶数对其忆阻值动态范围和输出电压动态幅值的影响规律, 推导出了磁滞旁瓣面积的计算公式. 结果表明, 分数阶导数阶数对磁滞回线的形状及所围成区域面积有重要影响. 特别地, 在外激频率大于1时, 分数阶忆阻器的记忆强度达到最大. 然后讨论了此分数阶忆阻器与电容或电感串联组成的单口网络的伏安特性. 结果表明, 在周期激励驱动时, 随着分数阶导数阶数的变化, 此分数阶忆阻器与电容的串联电路呈现出纯电容电路与忆阻电路的转换, 而它与电感的串联电路则呈现出纯电感电路与忆阻电路的转换.     

A general method to describe forgetting effect of memristors

Building suitable memristor models is essential when memristors are attractive to researchers and play a vital role in fields such as neuromorphic computing. The forgetting effect, which is usually used to mimic forgetting process of biological synapses, should be considered during the modeling process. Several models have been proposed to describe forgetting effect. However, they have some deficiencies in describing forgetting effect, such as boundary problems. In this paper, a general method is presented to resolve these problems. The method is suitable for models that employ an inner state to describe the change of resistance and use a window function to constrain the inner state (e.g., Chang's model, Chen's model, and Berdan's model). When the reason of forgetting effect is considered as dopant diffusion in previous models, the method determines the value of window function and the change rate of inner state according to the integrated result of dopant drift and dopant diffusion. Simulation results indicate that the issues of previous models are solved when the proposed method is applied in these models.     

基于忆阻器的spiking神经网络在图像边缘提取中的应用

根据生物视觉系统的功能原理,用忆阻器模拟生物突触,结合忆阻器的记忆特性和spiking神经网络的高效处理能力,构造了一种可用于图像边缘提取的三层spiking神经网络模型,该网络用忆阻器电导的变化量来表征图像边缘信息,仿真结果表明,该方法的边缘提取结果具有连续性、光滑性、低误检漏检性和边缘定位准确性,该神经网络的处理过程符合生物信息处理机制,为视觉系统的仿生实现提供了新的思路。     

荷控忆阻器等效电路分析模型及其电路特性研究

忆阻器是物理上新实现的具有记忆特性的基本二端电路元件. 根据φ-q关系式的泰勒级数形式构建了荷控忆阻器等效电路分析模型, 以三次非线性荷控忆阻器模型为例, 对不同参数条件下的荷控忆阻器进行了伏安关系、有无源性等电路特性的理论分析. 结果表明: 荷控忆阻器的伏安关系具有斜体“8”字形紧磁滞回线特性, 随其参数符号的不同, 荷控忆阻器呈现出无源性和有源性, 导致其电路特性发生相应的变化; 相比无源荷控忆阻器, 有源荷控忆阻器更适用于作为二次谐波信号产生电路使用. 制作了荷控忆阻器特性分析等效电路的实验电路, 实验测量结果很好地验证了理论分析结果. 关键词： 荷控忆阻器 等效电路 伏安关系 电路特性     

Dynamical characteristics of an HP memristor based on an equivalent circuit model in a chaotic oscillator

To develop real world memristor application circuits,an equivalent circuit model which imitates memductance(memory conductance) of the HP memristor is presented.The equivalent circuit can be used for breadboard experiments for various application circuit designs of memristor.Based on memductance of the realistic HP memristor and Chua's circuit a new chaotic oscillator is designed.Some basic dynamical behaviors of the oscillator,including equilibrium set,Lyapunov exponent spectrum,and bifurcations with various circuit parameters are investigated theoretically and numerically.To confirm the correction of the proposed oscillator an analog circuit is designed using the proposed equivalent circuit model of an HP memristor,and the circuit simulations and the experimental results are given.     

忆阻混沌振荡器的动力学分析

忆阻器(memristor)是一种有记忆功能的非线性电阻器,它是除电阻器、电容器和电感器之外的第四种基本电路元件.采用一个具有光滑磁控特性曲线的忆阻器和一个负电导替换蔡氏振荡器中的蔡氏二极管,导出了一个基于忆阻器的振荡器电路.采用常规的动力学分析手段研究了电路参数和初始条件变化时该光滑忆阻振荡器的动力学特性.研究结果表明,光滑忆阻振荡器与一般的混沌系统完全不同,它的动力学行为除了与电路参数有关外,还极端依赖于电路的初始条件,存在瞬态混沌和状态转移等奇异的非线性物理现象.     

纳米级尺寸参数对钛氧化物忆阻器的特性影响

随着忆阻器研究的不断深入, 忆阻器的研究已经进入微观阶段, 包括忆阻器内部结构的探究、内部粒子间的运动规律、各参数对忆阻器特性的影响等. 然而, 这些成果中没有关于尺寸参数对忆阻器特性影响的研究, 而尺寸参数是忆阻器成功制备的关键因素之一, 这大大限制了忆阻器的发展和实际应用. 本文从欧姆电阻定律入手, 从理论角度详细分析了尺寸参数对惠普忆阻器以及自旋忆阻器的性能影响. 在此基础上进行了一系列电路仿真实验, 得到不同尺寸参数下忆阻器的相关特性曲线. 文中各选取其中最具代表性的四组实验结果进行展示, 对这些结果进行了详细分析, 得到了惠普忆阻器工作的最佳尺寸范围在8-12 nm之间以及自旋忆阻器工作的最佳尺寸范围在500-600 nm 之间的结论. 实验结果不仅可为实际运用提供有力的支持, 同时也将为进一步研制钛氧化物忆阻器器件和相关理论工作提供重要的实验基础和理论依据.     

Agreement Dynamics of Memory-Based Naming Game with Forgetting Curve of Ebbinghaus

We propose a memory-based naming game （MBNG） model which is like some previous opinion propagation models. with two-state variables in full-connected networks, It is found that this model is deeply affected by the memory decision parameter, and then its dynamical behaviour can be partly analysed by using numerical simulation and analytical argument. We also report a modified MBNG model with the forgetting curve of Ebbinghaus in the memory. With deletion of one parameter in the MBNG model, it can converge to success rate S（t） = 1 and the average sum E（t） is decided by the size of network N.     

Discrete Memristor and Discrete Memristive Systems

In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G–L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The “∞”-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field.     

SPICE modeling of memristors with multilevel resistance states

With CMOS technologies approaching the scaling ceiling, novel memory technologies have thrived in recent years, among which the memristor is a rather promising candidate for future resistive memory (RRAM). Memristor’s potential to store multiple bits of information as different resistance levels allows its application in multilevel cell (MCL) technology, which can significantly increase the memory capacity. However, most existing memristor models are built for binary or continuous memristance switching. In this paper, we propose the simulation program with integrated circuits emphasis (SPICE) modeling of charge-controlled and flux-controlled memristors with multilevel resistance states based on the memristance versus state map. In our model, the memristance switches abruptly between neighboring resistance states. The proposed model allows users to easily set the number of the resistance levels as parameters, and provides the predictability of resistance switching time if the input current/voltage waveform is given. The functionality of our models has been validated in HSPICE. The models can be used in multilevel RRAM modeling as well as in artificial neural network simulations.     

基于Au/TiO_2/FTO结构忆阻器的开关特性与机理研究

采用简单的一步水热法在FTO导电玻璃上外延生长了锐钛矿TiO_2纳米线,制备了具有Au/TiO_2/FTO器件结构的锐钛矿TiO_2纳米线忆阻器,系统研究了器件的阻变开关特性和开关机理.结果表明,Au/TiO_2/FTO忆阻器具有非易失的双极性阻变开关特性.同时,在103s的时间内,器件在0.1 V的电阻开关比始终保持在20以上,表明器件具有良好的非易失性.此外,器件在低阻态时遵循欧姆导电特性,而在高阻态时则满足陷阱控制的空间电荷限制电流传导机制,同时提出了基于氧空位导电细丝形成与断开机制的阻变开关模型.研究结果表明Au/TiO_2/FTO忆阻器将是一种很有发展潜力的下一代非易失性存储器.     

忆阻混沌电路的分析与实现

具有记忆功能的忆阻器是除电阻器、电容器和电感器之外的第四种基本二端电路元件. 提出了由φ-q平面上的一条三次单调上升的非线性曲线来确定的光滑磁控忆阻器,它有着斜"8"字形的类紧磁滞回线的伏安特性曲线. 采用此忆阻器和负电导构成的有源忆阻器替换蔡氏混沌电路中的蔡氏二极管,导出了一个基于忆阻器的混沌振荡电路. 此外,利用常规的运算放大器和乘法器等元器件给出了有源忆阻器的等效电路实现形式. 理论分析、数值仿真和电路仿真结果一致,均表明忆阻混沌电路的动力学行为依赖于忆阻器的初始状态,在不同初始状态下存在混沌振荡、周期振荡或稳定的汇等不同的运行轨道. 关键词： 忆阻器 混沌电路 初始状态 等效电路     

忆阻逾渗导电模型中的初态影响

逾渗网格模型是当前忆阻器件机理分析研究领域的热点之一, 但现有模型缺乏对初态设定的讨论. 本文对逾渗网格模型进行了简化, 并基于此, 通过电压激励步进的方式, 研究了不同初态对单极性忆阻开关元件中逾渗导电通道形成的影响, 分析了形成通道的动态过程以及相应的物理意义, 验证了忆阻开关元件高低阻态的阻值实际表现为高斯分布而非理想双值稳态; 而不同初态条件下, 忆阻开关元件导电通道的形状存在着不同的"树形"结构, 进而影响着其阻值的分布. 研究成果有助于进一步揭示忆阻器尚未明确的导电机理, 为今后对具体不同类型的忆阻元件的初态分析提供指导性作用. 关键词： 忆阻器 开关元件 逾渗模型 初态分析     

Impact of multiplexed reading scheme on nanocrossbar memristor memory’s scalability

Nanocrossbar is a potential memory architecture to integrate memristor to achieve large scale and high density memory.However,based on the currently widely-adopted parallel reading scheme,scalability of the nanocrossbar memory is limited,since the overhead of the reading circuits is in proportion with the size of the nanocrossbar component.In this paper,a multiplexed reading scheme is adopted as the foundation of the discussion.Through HSPICE simulation,we reanalyze scalability of the nanocrossbar memristor memory by investigating the impact of various circuit parameters on the output voltage swing as the memory scales to larger size.We find that multiplexed reading maintains sufficient noise margin in large size nanocrossbar memristor memory.In order to improve the scalability of the memory,memristors with nonlinear I–V characteristics and high LRS(low resistive state)resistance should be adopted.