IEEE Circuits and Systems Magazine - Q2 2018 - 36

The memristor is not a concrete nanodevice but, more generally,
a manifestation of permanent natural principle.

In 2008, by virtue of the HP laboratories, the vision
of L. Chua from 1971 that one day the memristor might
be fabricated as a physical device without internal
power supply became true [3]. However, at the time L.
Chua warns of the confusion between the terms invention (gadget = nanodevice manufactured in the HP labs)
and discovery (unfolding = memristance as a natural
principle). Inventing the aircraft is something different
from a revealing of a natural principle that enables not
only airplanes to fly. The successfully developed and
implemented nonvolatile TiO 2 nanodevice is something
other than a natural principle called the memristance.
L. Chua's lifework consists in revealing complex natural
principles that had existed before humans appeared
and which take effect independently of us. He then left
it to others to utilize for inventing clever and useful applications the principles he had discovered.
Chua's memristor is therefore not an invention, even
if the word memristor appears on many U.S. patents. The
memristor, or, more exactly, the memristance as a permanent principle signifies, at least for Electrical Engineering, the state-dependent Ohm's law [4]:
v = R M (q) i, q =

# idt

(1)

Here v and i are the voltage and current, and R M is the
memristance or memory resistance; the term memory
denotes the ability to remember the amount of the passing charge q, which is the time integral of the current.
The memristor as a hypothetical element therefore models the memory effect in the systems. The resistance as
a system parameter is the final carrier of the memory.
It is not fixed but it depends on the state variable of the
system. This variable is of integrating nature, thus dependent on the history of the current according to (1).
Chua and Kang demonstrated in 1976 that the memristance, i.e. the state-dependent resistance, is in fact
the attribute of quite a number of existing systems, various in nature [5] such as thermistors, discharge tubes,
or ionic systems responsible for the operation of potassium and sodium channels in the Hodgkin-Huxley model
of the neural cell. Today we know that the memristance
takes effect in the operation of various types of resis-

tive switching memories, PCM (Phase Change Memories), and others. In all these cases, the resistance is the
carrier of the memory effect, but the state variables of
the system, determining the resistance, can be of various kinds, for example the temperature, width of the
tunneling channel of MIM (Metal-Insulator-Metal) junction, volume of the chalcogenide glass in the crystalline
state, etc. For the modeling of such phenomena, a more
general model of the memristive system is more useful,
because its memristance can depend on several internal
states given by physical variables other than the charge,
and also by the voltage or current. Also the equation of
motion is more complex than for the classical memristor (1), since it must truly model the often complicated
dynamics of the evolution of the states in the materials, for example the phase transitions in the PCM, etc.
The so-called current-controlled memristive system is
defined in [5] via a model containing the nonlinear functions R M and f:
v = R M (x, i ) i, xo = f (x, i )

(2)

The first equation again expresses Ohm's law, whereas the memristance R M depends on the current and on
the state vector x of potentially varied physical nature.
The second equation is a differential equation of motion
which expresses the dynamics of the associated dynamic system. It is obvious that Eq. (1) is a very special case
of Eq. (2). The system (2) with very weak or nonexistent
dependence of the R M on the state then models the classical memoryless resistive systems. According to this
approach, the memristance manifests itself to various
degrees of the memory effect virtually everywhere, for
example also in a simple wire whose resistance depends
on the state variable-the temperature.
Later on, L. Chua defined another two intermediate
stages in the classification of memristors (the so-called
ideal generic memristor and generic memristor) between
the memristor (1), now denoted as ideal memristor,
and the general memristive system (2), newly classified as extended memristor [6]. Their definitions
and self-explanations of the logic of the definitions
for the current-controlled elements are presented

Dalibor Biolek and Zdene
ˇ k Biolek are with the Department of Electrical Engineering/Microelectronics, University of Defence Brno/Brno University of
Technology, Brno, Czech Republic.

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