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
© 2016 John Wiley & Sons, Ltd.
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
Copyright © 2016 John Wiley & Sons, Ltd
Int. J. Numer. Model. 2017; 30: e2183
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