具有单纯形基函数的灵活的忆阻模型资源-CSDN文库

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根据提供的文件信息，我们可以从中提取出以下知识点： 1. 忆阻模型的定义与发展：忆阻器（Memristor）是一种基本的被动电子元件，它由电阻、电感和电容这三种被动元件之外的第四种元件。1971年首先由蔡少棠提出，它是根据通过元件的电荷和磁通的关系来定义的，即磁阻（memristance）与电荷是时间历史的函数。 2. 忆阻系统的定义：忆阻系统的概念是对忆阻器的推广。忆阻系统可以通过特定的基本电路变量作为输入和输出变量，来定义不同的记忆设备，如忆容系统和忆感系统。 3. 忆阻模型的关键元素：在文档中提到的忆阻模型中，采用了分段窗口函数限制状态变量的物理范围，同时使用了一个分段线性模型（称为单纯形基函数模型）来描述电流和电荷的积分函数。 4. 单纯形基函数模型的应用与优势：文中提出的忆阻模型因为单纯形基函数模型良好的逼近能力，显示出了很大的灵活性。通过这种模型，可以几乎解析地获得状态变量和忆阻值的表达式，从而避免了现有的一些忆阻模型在仿真过程中出现的严重错误。 5. 文档中涉及的研究成果发表信息：该研究成果发表在《国际数值建模杂志：电子网络、器件和场》上，论文编号为Int.J.Numer.Model.2017;30:e2183，于2016年7月14日在Wiley在线图书馆上在线发布，并且获得了相应的数字对象标识符（DOI: 10.1002/jnm.2183）。 6. 知识产权声明：文章的版权归John Wiley & Sons, Ltd.所有，文章的接收日期为2016年2月13日，修订日期为6月8日，接受日期为6月16日。 7. 论文关键词：这些关键词提供了对文档内容的概括，包括忆阻模型、窗口函数、分段线性逼近。 8. 忆阻器在电子和信息技术领域的应用前景：由于忆阻器和忆阻系统具有存储信息的能力，因此它们在新型存储器、神经网络模拟等领域的应用前景被广泛看好。 9. 文献引用信息：文中提到的忆阻器的首次提出是在1971年的文献[1]中，而忆阻系统的定义则在文献[2]中提出。通过上述内容的提取，我们可以构建一个关于忆阻器和忆阻系统的详细知识点框架，其中重点阐述了忆阻器的基本定义、忆阻系统的概念推广、以及忆阻模型在实际应用中的重要性。此外，也概述了提出灵活忆阻模型的研究背景和成果，以及该模型相较于其他模型的优势和特点。

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INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS

Published online 14 July 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/jnm.2183

A ﬂexible memristive model with simplex basis function

Juntang Yu

,

, Xiangming Xi and Shuning Wang

Department of Automation, Tsinghua National Laboratory for Information Science and Technology (TNList), Tsinghua

University, Beijing 100084, China

SUMMARY

In this paper, we propose a ﬂexible memristive model with simplex basis function. In the memristive model, a

piecewise window function is applied to limit the physical range of the state variable, and a piecewise linear model

(called simplex basis function model) is applied to describe the integral function of the current and charge. The

expression of the state variable and the memristance can be almost analytically obtained. Thus, some serious errors

occurring in the simulations of some existing memristive models can be avoided. The proposed memristive model

shows great ﬂexibility due to the good approximation capability of the simplex basis function model. Copyright

Received 13 February 2016; Revised 8 June 2016; Accepted 16 June 2016

KEY WORDS: memristive model; window function; piecewise linear approximation

1. INTRODUCTION

Firstly postulated in 1971 [1], memristor is considered as the fourth fundamental two-terminal passive

circuit element. The other three are the resistor, the inductor, and the capacitor. The memristor is

deﬁned to present the relation between the charge q and ﬂux ' through it, which is

d' D M dq (1)

where M is the resistance of memristor, called memristance. It follows that memristance M depends

on charge q, deﬁned as the time history of the memristor current.

As a generalization of memristor, memristive system is deﬁned in [2] by

Px D f.x;u;t/ (2a)

y D g.x; u; t/u (2b)

where u, y,andx denote the input, output, and state variables of the system, respectively, t denotes

the time variable, and f./ and g./ are functions of x, u,andt. With some speciﬁc basic circuit

variables as the input and output variables of a memristive system, different memory devices, such as

memcapacitive system and meminductive system, can be deﬁned [3].

Because the Hewlett–Packard labs ﬁrstly presented the physical memristor in 2008 [4], the promis-

ing device has attracted more and more attentions in various application ﬁelds, including nonvolatile

memories [5–7], neuromorphic systems [8–10], and nonlinear circuit applications [11, 12]. For these

applications, it is necessary to propose an accurate memristor model, which can be calculated

analytically.



Correspondence to: Juntang Yu, Department of Automation, Tsinghua National Laboratory for Information Science and

Technology (TNList), Tsinghua University, Beijing 100084, China.



E-mail: yjt11@mails.tsinghua.edu.cn

Int. J. Numer. Model. 2017; 30: e2183

1 of 9

J. YU, X. XI AND S. WANG

In [4], the physical memristor device is a semiconductor thin ﬁlm sandwiched between two metal

contacts. Let D, R

,andR

of f

denote the full length, low, and high resistances of this ﬁlm,

respectively. The mechanism model of this device is formulated as

v.t/ D



w.t/

C R

of f



1 

w.t/



i.t/ (3a)

dw.t/

D 

i.t/ (3b)

where 

is the average ion mobility in a uniform ﬁeld, w.t/ denotes the length of the high dopant

concentration region of the ﬁlm, and v.t/ and i.t/ denote the voltage and current of this device,

respectively.

In view of the physical range limitation of w.t/, a class of memristor models are proposed by

multiplying window functions on the right side of (3b), which can be characterized by

v.t/ D .R

x C R

of f

.1  x//i.t / (4a)

D ˛i.t/f .x/ (4b)

where the constant coefﬁcient ˛ D 

, the state variable x D w.t/=D,andf./ is a window

function of x. Many window functions have been used to model the memristor [4,13–17]. However, the

nonlinear characteristic of memristor cannot be fully described by these models. Actually, the behavior

of physical memristor devices such as in [18] is highly nonlinear and not consistent with these models.

Reviewing the mechanism of the memristor device, M. Pickett et al. propose a more accurate model,

called Simmons tunnel barrier (STB) model [19]. In this model, the state variable x is the STB width

between the metal electrode and the conducting channel generated by electroforming the TiO

device.

The derivative of state variable Px.t/ has an exponential dependence on the current i.t/, and it is too

complex to obtain the explicit solution of state variable x.t/. The state variable x.t/ depends on both

charge q.t/ and current i.t/, and so is the memristance M: Therefore, the model is a memristive

system.

To reduce the complexity of memristive model, a simpliﬁed model, called ThrEshold Adaptive

Memristor (TEAM) model, is presented in [20]. The derivative Px.t/ of the TEAM model depends on

both the state variable x.t/ and the current i.t/, and the state variable x.t/ is uncoupled from the

current i.t/. In the model, the functions of state variable x.t/ perform as the window functions to con-

strain the state variable x.t/ to the certain bounds. Compared with the STB model, the TEAM model

can signiﬁcantly improve the simulation runtime with sufﬁcient precision. However, it is still difﬁcult

to obtain the explicit solution of the state variable x.t/ or the memristance M: Thus, the numerical

methods have to be applied to solve the differential equations. There may exist some serious simulation

errors [16, 21], and the computational efﬁciency is limited. Other memristive models such as [22–24]

also suffer from the same problem.

In this paper, a ﬂexible memristive model is proposed to solve the problem. A piecewise window

function is applied to characterize the physical range limitation of the state variable x.t/, and a piece-

wise linear approximation model is applied to characterize the relationship between memristance M

and charge q.t/ and current i.t/. The solution of this memristive model can be almost analytically

obtained. The memristive model also shows great ﬂexibility.

2. MEMRISTIVE MODEL WITH SIMPLEX BASIS FUNCTION

Under the assumption of the separability of the current i.t/ and the state variable x.t/, the derivative

Px.t/ of a general memristive model can be formulated as

dx.t/

D f

.x.t //  f

.i.t// (5)

DOI: 10.1002/jnm

2 of 9

Int. J. Numer. Model. 2017; 30: e2183

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