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 fractionalorder 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.

Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit

We propose a novel circuit for the fractional-order memristive neural synaptic weighting(FMNSW).The introduced circuit is different from the majority of the previous integer-order approaches and offers important advantages. Since the concept of memristor has been generalized from the classic integer-order memristor to the fractional-order memristor(fracmemristor), a challenging theoretical problem would be whether the fracmemristor can be employed to implement the fractional-order memristive synapses or not. In this research, characteristics of the FMNSW, realized by a pulse-based fracmemristor bridge circuit, are investigated. First, the circuit configuration of the FMNSW is explained using a pulse-based fracmemristor bridge circuit. Second, the mathematical proof of the fractional-order learning capability of the FMNSW is analyzed. Finally, experimental work and analyses of the electrical characteristics of the FMNSW are presented. Strong ability of the FMNSW in explaining the cellular mechanisms that underlie learning and memory, which is superior to the traditional integer-order memristive neural synaptic weighting, is considered a major advantage for the proposed circuit.

A Large Dynamic Range Floating Memristor Emulator With Equal Port Current Restriction

In this paper, a large dynamic range floating memristor emulator(LDRFME) with equal port current restriction is proposed to be achieved by a large dynamic range floating voltage-controlled linear resistor(VCLR). Since real memristors have not been largely commercialized until now, the application of a LDRFME to memristive systems is reasonable. Motivated by this need, this paper proposes an achievement of a LDRFME based on a feasible transistor model. A first circuit extends the voltage range of the triode region of an ordinary junction field effect transistor(JFET). The idea is to use this JFET transistor as a tunable linear resistor. A second memristive non-linear circuit is used to drive the resistance of the first JFET transistor. Then those two circuits are connected together and, under certain conditions, the obtained "resistor" presents a hysteretic behavior,which is considered as a memristive effect. The electrical characteristics of a LDRFME are validated by software simulation and real measurement, respectively.

类脑计算的基础元件:从忆阻元到分忆抗元

讨论一种新颖的类脑计算的基础元件:分忆抗元(分数阶忆阻元).忆阻元的概念从经典的整数阶推广到分数阶忆阻元,即分忆抗元.分忆抗元是分数阶忆阻元的一个合成词.分忆抗值是分忆抗元的分数阶阻抗.因此,可以很自然地想到一系列具有挑战性的理论难题:分忆抗元和传统的分抗元以及著名的忆阻元的关系是什么;关于介于忆阻元和电容元或电导元之间的内插特性是什么;以及关于分忆抗元在蔡氏电路周期表中的位置在哪里;任意阶理想的容性分忆抗元和感性分忆抗元的分忆抗值的一般表达式是什么;分忆抗元的度量单位和物理量纲是什么;鉴别分忆抗元的指纹特征是什么;如何通过普通的忆阻和电容与电感以模拟电路形式有效实现任意分数阶忆阻元.基于大量的前期探索性研究成果,对上述一系列理论难题进行了初步探讨.分忆抗元解决了分抗元很难实现记忆端口电荷或磁通量的功能,而且分忆抗元可作为一种基本电路元件应用到混沌系统、神经元电路、神经网络电路等的设计.

电路元件周期表——蔡氏周期表与新型记忆元件

在介绍蔡氏周期表的基础上,给出已有电路元件(电阻、电容、电感、忆阻、忆容、忆感、分抗和分忆抗元等)在周期表中的位置。近年来,“分数阶忆阻”的概念开始逐渐出现在文献中,但其概念并不统一。本文将已有的分数阶忆阻及电路总结为4种,并确定对应的元件在蔡氏周期表中的位置。分数阶积分是表征有损记忆的有力工具,本文不仅给出电路元件禀赋关系统一表示式,还给出分数阶积分控制式记忆元件——电流分数阶积分控制式忆容(CFMC)、电压分数阶积分控制式忆容(VFMC)、电流分数阶积分控制式忆感(CFMI)、电压分数阶积分控制式忆感(VFMI)、电流分数阶积分控制式分忆抗(CFFM)、电压分数阶积分控制式分忆抗(VFFM)等的定义,并给出部分分数阶积分控制式记忆元件的运算结构图。

离散分数阶忆阻系统建模及其在Logistic映射中的应用

为了拓宽忆阻器的研究范围,通过分析分数阶差分理论和三次非线性磁控忆阻器数学模型,建立了由分数阶差分方程确定磁通量的离散分数阶忆阻模型。数值模拟结果显示,紧缩磁滞回线具有忆阻器的三个特征,这表明所提出的离散分数阶忆阻器满足忆阻器的定义。最后,作为应用,设计了分数阶忆阻Logistic映射,并得到了系统在特定初值和阶次下的多稳定性和新的混沌序列。建立的忆阻模型输入电流不再局限于连续信号,并且将阶次推广至分数阶,拓宽了忆阻器的研究范围。