IEEE Circuits and Systems Magazine - Q2 2018 - 39

In August 2008, just after the discovery of the HP memristor, L. Chua gave an interview for the EE Times [9], and
here he used the term Fingerprint as an identification sign
of the memristor. Such a fingerprint, serving to recognize
memristive behavior from experimental data, is the v - i
pinched hysteresis loop appearing under bipolar excitation. Such characteristics appeared before 2008 in journals particularly from the areas of physics, biophysics,
and materials engineering. Now their common principle
could be identified: their memristive nature.
It is worth noting that prior to the term fingerprint the
term hallmark was used. In connection with the pinched
hysteresis loop, the term hallmark was used five years
earlier in [10]. In November 2008, during the memorable
Memristor and Memristive Systems Symposium in Berkeley [11], L. Chua introduces the pinched hysteresis loop as
an important fingerprint of every memristive system. This
and some other fingerprints were published before in [2]
and [5] as separate Theorems. After 2008, these pieces

.
.
-2

.
? .

TIF v (-2)

i (-2)

TIQ

of knowledge were completed and specified [4], [12], [13].
Over time, other fingerprints were recognized and published [14], [15], and this trend is continuing [16]-[18]. A
brief summary is given in Table 2.
The fingerprints that every memristor from Table 1
should comply with are summarized in [19]. They can be
paraphrased as follows (for details see [19]):
The system exhibits hysteresis loops pinched at the
v - i origin when driven by a bipolar periodical signal. Above a certain critical frequency, the hysteresis lobe area monotonically decreases to zero as
frequency increases towards infinity and thus the
hysteresis curve shrinks a to single-valued function
at infinite frequency.
The fingerprints must hold under any circumstances,
i.e. for any levels and any frequency of the excitation,
and for any initial states of the element.

.
.
-2

α

Table 2.
History of memristor fingerprints.

β
d
dt

-1

d
dt

Flux v (-1)

Year

Fingerprint (FP)

1971

Pinched Hysteresis Loop (PHL)

A note in
Conclusion [2]

1976

PHL

[5]

Double-valued PHL
PHL symmetry

i (-1) Charge -1

α

Note

Shrinking the PHL to line
(frequency FP)
2003

"Pinched" HL

The term
"hallmark of
memristor" [10]

2008

"Pinched" HL

The first
appearance
of the term
"fingerprint" [9],
[11]

2011

Shrinking the PHL to curve

[4]

Odd-symmetric PHL*

[12]

Diminishing the area of PHL

[13]

DC steady state*

[14]

DC pseudo-steady state*

[15]

β
d
dt

d
dt

0 Voltage v

i
?

α

Current 0

?
β

2012
d
d
dt
dt
?
1
1 d /dt v (1)
i (1) d /dt
.
. Voltage
Current .
.
.
.
Figure 2. Illustration of the storeyed structure of fundamental
elements. the ground floor, built on the v, i basement, is occupied by the classical r, C, L elements, and their memory
versions are located upstairs. For simplicity, the elements interconnecting the constitutive variables belonging to different
floors, e.g. the (a, b) = (0,-2) element etc. are omitted.

SECOND quartEr 2018

2013

PHL without trans. phenomena*
2015

*

Specification of the way of
diminishing the area of PHL*

[16]

Variation of "frequency FP"*

[17]

Homothety FP*

[18]

The given fingerprint is a fingerprint of ideal memristor.

IEEE CIrCuItS aND SyStEmS magazINE

39



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