Everything You Wish to Know About Memristors
But Are Afraid to Ask
Leon CHUA
Dept. of EECS, University of California, Berkeley, CA 94720, California, USA
Dept. of EEE, Imperial College London, SW7 2AZ, London, UK
EC Marie Curie Fellow, School of Computing, University of Kent, CT2 7NZ,
Canterbury, UK
chua@berkeley.edu
Abstract. This paper classifies all memristors into three
classes called Ideal, Generic, or Extended memristors.
A subclass of Generic memristors is related to Ideal mem-
ristors via a one-to-one mathematical transformation, and
is hence called Ideal Generic memristors. The concept of
non-volatile memories is defined and clarified with illus-
trations. Several fundamental new concepts, including
Continuum-memory memristor, POP (acronym for
Power-Off Plot), DC V-I Plot, and Quasi DC V-I Plot, are
rigorously defined and clarified with colorful illustrations.
Among many colorful pictures the shoelace DC V-I Plot
stands out as both stunning and illustrative. Even more
impressive is that this bizarre shoelace plot has an exact
analytical representation via 2 explicit functions of the
state variable, derived by a novel parametric approach
invented by the author.
Keywords
Memristor, discrete-memory memristors, continuum-
memory memristor, POP, Power-Off Plot, DC V-I
Plot, Quasi DC V-I Plot, Shoelace V-I Plot, paramet-
ric approach, graphical composition, piecewise-linear
(PWL) function
1. Some Nagging Questions about
Memristors
Ever since the publication of the hp’s seminal paper
in Nature [1], reporting its fabrication of a 2-terminal de-
vice that bears the fingerprints of the memristor [2], there
has been a torrent of memristor activities from both indus-
try and academia to exploit the unique properties of the
memristor for building a new generation of smart com-
puters [3] and brain-like machines [4], [35]. Since the
memristor is intrinsically a nonlinear electronic device,
researchers and engineers unfamiliar with nonlinear
dynamics are often confused, if not intimidated. Following
are some questions researchers and engineers are afraid
to ask:
1. How do I know whether my experimental device is
a memristor ?
2. What are the fingerprints of a memristor?
3. Does memristor possess a signature that distinguishes
it from the 3 classic circuit elements (resistor, ca-
pacitor, inductor)?
4. What is a non-volatile memory?
5. Is every memristor a non-volatile memory?
6. What unique attribute of the memristor is exploited to
make a non-volatile memory?
7. How does one write a binary bit “0”, or “1”, on
a memristor?
8. How does one read a binary bit “0”, or “1”, from
a memristor?
9. What does it mean to say the memristor can store
analog data?
10. Most 2-terminal solid state devices, such as the p-n
junction diode, have a DC V-I curve. What does the
DC V-I curve of a memristor look like?
11.Can we store energy on a memristor?
12.Why are synapses memristors?
13.Why are the sodium and potassium ion channels in
the classic Hodgkin-Huxley axon membrane model
not time-varying resistors, but are in fact memristors?
14.Why are brains made of memristors?
2. Experimental Definition of
Memristors
Any 2-terminal device exhibiting a pinched hysteresis
loop which always passes through the origin in the volt-
age-current plane when driven by any periodic input cur-
rent source, or voltage source, with zero DC component is
called a memristor1
. If the input is a current source, it is
called a current-controlled memristor as shown in Fig. 1. If
it is a voltage source, it is called a voltage-c
