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The document discusses the characterization of memristors, highlighting their diverse material composition and presence in various living organisms. It introduces a mathematical model to approximate the measured hysteresis loops and categorizes memristors into four classes based on the complexity of their mathematical representation. The document also presents the constitutive relations for charge-controlled and flux-controlled memristors.

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6 views1 page

R 3

The document discusses the characterization of memristors, highlighting their diverse material composition and presence in various living organisms. It introduces a mathematical model to approximate the measured hysteresis loops and categorizes memristors into four classes based on the complexity of their mathematical representation. The document also presents the constitutive relations for charge-controlled and flux-controlled memristors.

Uploaded by

greyffox777
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Characterization of laser thermal loading on

because the internal composition of the device is irrele-


vant. Indeed, not only can memristors be made from differ-
ent materials, they have even been found in amoeba, squids
and plants, and numerous other living beings [5].
Once a device is identified from experimental
measurements to be a memristor, it is natural to develop
a mathematical model which can mimic approximately the
measured pinched hysteresis loops.
For pedagogical reasons, it is convenient to classify
a memristor according to the complexity of its mathemati-
cal representation into the 4 classes listed in Tab. 1, in the
order of decreasing complexity.
The Venn diagram in Fig. 3 shows the memristor
universe and the relationship among the 4 classes of mem-
ristors listed in Tab. 1.
The simplest class of memristors defined in the lowest
part of Tab. 1 is called an ideal memristor, which coincides
with the original definition postulated in [2]. Indeed, we
can recover its constitutive relation, within an arbitrary
constant (0),via
0 (0) ( ) ( ) ˆ q
   R d qq q    . (1)
Observe that differentiating both sides of (1) with
respect to time t gives
  d d R
dt t q d
 q  (2)
or
v  Rq i (3)
upon identifying d
v
dt
  and dq
dt  i , respectively.
Equation (1), which is equivalent to (2), is called the
constitutive relation of a charge-controlled memristor in
[2], [6], [7]. The dual constitutive relation of a flux-con-
trolled memristor
q q  ˆ (4)
is equivalent to the voltage-controlled memristor
i  G( )  v , (5)

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