一种忆感器模型及其振荡器的动力学特性研究

忆感器是在忆阻器基础上定义的一种新型记忆电路元件. 在实际忆感器尚未实现的情况下, 为探索忆感器及其在非线性电路中的特性, 提出了一种忆感器数学模型和电路模型. 基于该模型设计了一个非线性振荡电路, 采用理论分析、仿真分析和实验验证的方法研究了忆感器模型的特性及其在电路中的动力学规律. 分岔分析表明, 在适当的参数下忆感器会使电路产生周期和混沌振荡. 设计了实现忆感器模型及其振荡器的模拟电路, 实验验证了忆感器模型和振荡器的特性, 实验结果与理论分析完全一致.     

一个通用的记忆器件模拟器

本文根据惠普忆阻器模型提出了一个新的接地忆阻器模拟等效电路.并以此为基础,采用常规的电子元件构建了一个通用的记忆器件模拟器.该模拟器能在电路拓扑结构不变的情况下,通过改变接入元件的性质能将接地忆阻器分别转化为浮地忆阻器、浮地忆感器和浮地忆容器.由于该模拟器是浮地的,因而可以方便的与其他电子器件实现灵活的连接形式.Pspice仿真实验验证了模拟器的真确性和有效性.     

基于模拟电路的新型忆感器等效模型

本文首先利用光敏电阻阻值的可控性, 建立了磁通控制型忆阻器的等效电路模型. 通过对忆感器和忆阻器间转换关系的分析, 采用模拟电子元器件设计了磁通控制型忆感器的实用等效电路模型, 给出了理论分析并结合Pspice软件进行了仿真验证. 忆感器等效电路模型的韦安关系展现出典型的非线性磁滞回线特性. 最后, 运用实验手段研究了正弦波和三角波两种典型电压信号激励下忆感器与RC串联后电路的动态特征, 证明了本文提出忆感器等效电路模型的有效性. 关键词： 忆阻器 忆感器 磁滞回线特性 Pspice     

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.     

基于Knowm忆阻器的新型忆感器模型的设计与分析

以往有关忆阻器模型及其应用研究主要集中于忆阻器基本概念构建并分析忆阻器模型及其等效电路模型,而基于市场上商用忆阻器件的研究则很少.本文根据忆感器与忆阻器之间的理论关系,基于全球首款商用忆阻器芯片:Knowm忆阻器,结合第二代电流传输器和跨导运算放大器,构建了一种新型忆感器模型.通过调节输入信号的频率和幅值以及运算跨导放大器的跨导增益,可有效地在电路中实现忆感器忆感值的连续调节.设计了新型忆感器的LTspice电路模型和硬件实验电路,以电路仿真结果和硬件电路实验结果验证了新型忆感器模型的有效性和设计方法的正确性.     

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     

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     

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.     

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.     

离散忆阻混沌系统的Simulink建模及其动力学特性分析

为拓广离散忆阻器的研究与应用,基于差分算子,构建了具有平方非线性的离散忆阻模型,并实现了Simulink仿真.仿真结果表明,设计的忆阻器满足广义忆阻定义.将得到的离散忆阻引入三维混沌映射中,设计了一种新型四维忆阻混沌映射,并建立了该混沌映射的Simulink模型.通过平衡点、分岔图、Lyapunov指数谱、复杂度、多稳态分析了系统复杂动力学特性.本文从系统建模角度出发,构建离散忆阻与离散忆阻混沌映射,进一步验证了离散忆阻的可实现性,为离散忆阻应用研究奠定了基础.     

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.     

A flux-controlled model of meminductor and its application in chaotic oscillator

A meminductor is a new type of memory device developed from the memristor.We present a mathematical model of a flux-controlled meminductor and its equivalent circuit model for exploring the properties of the meminductor in a nonlinear circuit.We explore the response characteristics of the meminductor under the exciting signals of sinusoidal,square,and triangular waves by using theoretical analysis and experimental tests,and design a meminductor-based oscillator based on the model.Theoretical analysis and experiments show that the meminductor-based oscillator possesses complex bifurcation behaviors and can generate periodic and chaotic oscillations.A special phenomenon called the co-existent oscillation that can generate multiple oscillations(such as chaotic,periodic oscillations as well as stable equilibrium) with the same parameters and different initial conditions occurs.We also design an analog circuit to realize the meminductor-based oscillator,and the circuit experiment results are in accordance with the theory analysis.     

基于磁电耦合效应的基本电路元件和非易失性存储器

磁电耦合效应是指磁场控制电极化或者电场控制磁性的物理现象,它们为开发新型电子器件提供了额外的物理状态自由度,具有巨大的应用潜力.磁电耦合系数作为磁电耦合材料的重要参量,体现了材料磁化和电极化的耦合性能,其随外加物理场的变化可以表现出非线性回滞行为,具备作为非易失存储的物理状态特征.本文讨论了基于磁电耦合效应如何建立起电荷-磁通之间的直接关联,继而实现了第四种基本电路元件并构建了完整的电路元件关系图.在此基础上,研究了多铁性异质结中的非线性磁电耦合效应,并利用其独特的电荷-磁通关联特性,开发了基于磁电耦合系数的电写-磁读型非易失性信息存储、逻辑计算与类神经突触记忆等一系列新型信息功能器件.     

Realization of a flux-driven memtranstor at room temperature

The memtranstor has been proposed to be the fourth fundamental circuit memelement in addition to the memristor,memcapacitor, and meminductor. Here, we demonstrate the memtranstor behavior at room temperature in a device made of the magnetoelectric hexaferrite(Ba_(0.5)Sr_(1.5)Co_2Fe_(11) AlO_(22)) where the electric polarization is tunable by external magnetic field. This device shows a nonlinear q–р relationship with a butterfly-shaped hysteresis loop, in agreement with the anticipated memtranstor behavior. The memtranstor, like other memelements, has a great potential in developing more advanced circuit functionalities.     

Memcapacitor model and its application in a chaotic oscillator

A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memcapacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and experiments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations.In addition, based on the digital signal processing(DSP) technology, a scheme of digitally realizing this memcapacitor oscillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology(NIST). The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system.     

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.