Does the D.C. Response of Memristors Allow Robotic Short-Term
Memory and a Possible Route to Artiﬁcial Time Perception?*
Ella Gale1,2, Ben de Lacy Costello1 and Andrew Adamatzky1,2
Abstract— Time perception is essential for task switching,
and in the mammalian brain appears alongside other processes.
Memristors are electronic components used as synapses and
as models for neurons. The d.c. response of memristors can
be considered as a type of short-term memory. Interactions
of the memristor d.c. response within networks of memristors
leads to the emergence of oscillatory dynamics and intermittent
spike trains, which are similar to neural dynamics. Based on
this data, the structure of a memristor network control for
a robot as it undergoes task switching is discussed and it is
suggested that these emergent network dynamics could improve
the performance of role switching and learning in an artiﬁcial
intelligence and perhaps create artiﬁcial time perception.
I. INTRODUCTION
Robots need artiﬁcial perception to be able to plan for the
future, learn from the past and make intelligent judgements in
the present [1], furthermore temporal concepts are needed for
an agent to comprehend its environment and to successfully
communicate with humans in a meaningful manner [2].
Time perception covers several essential concepts which are
needed for many tasks: duration of a task, perceived simul-
taneity of events with a small delta of time between them
and ordering of events [1]. For example, to enable robots
to switch tasks quickly between two (or more) different
behaviours [1], the robot needs some concept of different
rules at different time states.
There has not been a great deal of work on artiﬁcial
time perception and in studying human time perception we
must turn to both neuroscience and philosophy. Robotics has
drawn from these two areas, with a recent paper looking at
the underlying structure of neural nets with regards to time-
perception and rule switching plasticity [1]. Wittgenstein
famously argued that a thought was impossible without a
language containing that thought’s concepts [3] and another
recent paper looked at getting robots to develop their own
language for time concepts [2], which interestingly involved
errors due to individual robot’s map not being entirely
congruent with each other (a concept behind many human
misunderstandings and conﬂict). In this paper, we will take
the neuroscience view and consider the structure of an
artiﬁcial ‘brain’ that could understand temporal concepts.
In the brain, the time-perception tends to ‘ride along’
with other mental processes: there is no part of the brain
*This work was supported by EPSRC grant number EP/H01438/1
1E.
Gale,
B.
de
Lacy
Costello
and
A.
Adamatzky
are
part
of
the
Unconventional
Computing
Group,
University
of
the
West
of
England,
Bristol,
BS16
1QY,
England
{ella.gale,ben.delacycostello,andrew.adamatzky}@uwe.ac.uk
2E.Gale and A. Adamatzky are also afﬁliated with the Bristol Robotics
Laboratory, Bristol, BS16 1QY, England
that is speciﬁcally evolved to deal with time perception [1]
and different parts are associated with temporal aspects of
behaviour on different timescales [10]. Instead, time seems
to be perceived relative to internal neurological changes [11]
as is evidenced by how it can be disrupted by disease [12].
The operation of time perception thus seems related to the
network dynamics of the brain.
The memristor is the 4th fundamental circuit element [5]
which is essentially a resistor with memory, and which, in
1971, was predicted (based on both electromagnetic and
circuit theory) to be a two-terminal circuit element with
a constitutive relation that would relate magnetic ﬂux to
charge. Although the constitutive relation technically covers
everything about a circuit element’s operation, this theory
offered little clue of how to build such a device. Thus, the
memristor was only related to an actual device in 2008 [4],
even though memristors had been previously experimentally
studied and commercially investigated under the moniker
of ReRAM. There are two different theories that model
experimental memristor’s operation: the phenomenological
model [4], which is based on a 1-D model of variable
resistors and which has been the basis of more complex
models (such as those which include non-linear drift [?]
or window functions) and many simulations (such as [?]);
and the memory-conservation model (see
[13] for a full
description or [14] for a summary) which is based on the
electrodynamics of a 3-D model of variable resistors and
ﬁts with the constitutive relation. Recent simulations have
shown that memristors can be used as synapses with artiﬁcial
spiking neurons [6], [7], theoretical results have demon-
strated that action potential transport in real neurons can be
modelled using memristors [8] and ﬁnally recent work [9]
has highlighted the memristors native spiking ability, all of
which suggest memristors could be the basis of synthetic
neuron analogues for use in an artiﬁcial brain.
In this short paper we will summarise some recent relevant
memristor results and discuss how memristor networks might
provide a route to incorporating time perception into an
artiﬁcial brain/intelligence in a bio-mimetic or even human-
like manner.
II. MEMRISTOR’S SHORT-TERM MEMORY
Memristors are commonly thought to be a.c. components.
The pinched hysteresis loop used to identify a memristor is
usually plotted in V −I space, however this description is not
complete without inclusion of the aspect of time-dependence.
In a.c. systems this is evidenced as the dependence of the
Lissajous curve lobe size on the voltage waveform frequency
arXiv:1402.4007v1  [cs.RO]  17 Feb 2014
(and is why memristor papers now tend to include a graph
showing this). This time dependence is due to the memory
property of the device responding slower than the frequency
of the voltage change (see [13] for a discussion of what
this memory property might be) and this memory property
must have some characteristic time scale, τ, associated with
it that relates to the fundamental frequency, ω0 at which the
a.c. voltage input produces the maximum hysteresis in the
memristor I −V curve.
In steady voltage circuits (i.e. d.c. voltage input), we
suggest that the time dependence is the commonly-observed
current transients as seen when the voltage changes or is
switched on or off, ∆V . Figure 1 taken from [15] shows
an example current spike response to a step voltage. The
characteristic timescale is related to the time taken for the
spike to decay. As ∆V →δV and we go from d.c. steps
to an a.c. smooth curve with a set frequency, we can see
that this characteristic timescale response is related to the
hysteretic lag.
Fig. 1.
An example of a typical I −t spike proﬁle as taken from [15]. The
characteristic timescale, τ, is around 3.5-4s, marked on are the timescales
for decay to a percentage of peak height: red line τ50 (decay to 50%),
orange line τ90, green τ95 and grey τ99.
Whilst the memristor is responding to a voltage change,
it is in a different state to a memristor that has responded:
this is a form of memory. Speciﬁcally, it is a short term
memory rather than a long-term memory or stateful response,
this short-term memory could be used as a form of working
memory. If a second spike is input into the system, it reacts
differently as a result of the previous spike if and only if the
second spike is happens within time τ.
The memory-conservation model of memristance [13]
introduces the concept of a second charge carrier, the ionic
charge carrier, in addition to the electrons. This ionic charge
carrier has a different mobility, speed and inertia to electrons
and therefore takes longer to respond to voltage changes.
Thus, in [13] it is claimed that the lag which causes the
memristor hysteresis under a.c. is due to the slower response
time of the ionic charge carriers, and this is investigated
in a forthcoming paper. The slow ionic charge response is
apparent in the d.c. response as the decay of the I −t curve.
The characteristic timescale is a measure of the ionic charge
carrier’s slower response to a voltage change (which we
expect will be related to it’s ionic mobility) and it measures
when the ionic effect is negligible. Therefore, if a second
spike is received within time τ, the ionic charge carrier hasn’t
recovered and responds at a different level than would be
otherwise expected.
III. NETWORKS OF MEMRISTORS
A. SIMULATION
What could such a short term memory be used for? A
recent simulation based on the experimental observations
outlined earlier showed that networks of memristors can
learn, change and adapt [16]. Memristor networks were
designed and simulated with the purpose of composing
and performing music. Each network node was a note (in
terms of function) and a source drain or sink (in terms
of modelled component), each connection a transition from
one note to the other (function) and a pair of antiparallel
memristors (component). The normalised conduction proﬁle
of a memristor under d.c. voltage as modelled using the
memory-conservation model [13] was descretized and used
as a look-up table of how connection weight changed each
time a connection was used.
The network was capable of being seeded to produce
music similar to the seed genre. Crucially, the memristor
network continued to change and adapt as it was used. This
shows a similar plasticity to the brain and a very simple
type of Hebbian learning. This is different to evolutionary
techniques because the learning is a result of using the
networks rather than being directed by similarity to a ﬁtness
function or desired output.
Although this experiment serves to demonstrate how a
composing memristor machine could be built, there are
similarities in the structure to the brain, which is also a learn-
ing network. It has been suggested that building a creative
computer could require the almost accidental building of a
brain-like computer.
B. EXPERIMENT
Fig. 2.
The three memristor circuit used to generate the output in ﬁgure 3
Experimental data of highly simpliﬁed TiO2 sol-gel mem-
ristor networks show some intriguing similarities to the
dynamics of the brain. A simple ‘network’ of just three
memristors (arranged as in ﬁgure 2) put under a constant
positive d.c. voltage shows a current response similar to that
shown in ﬁgure 3. Here we see sudden and large spiking
responses against a background of an emergent oscillation,
this is interesting as it even includes the measurement of
Fig. 3.
Brainwave like oscillations and spike trains that emerged from
the circuit in ﬁgure 2, as taken from [16]. Utilising these dynamics could
provide a route build a neuromorphic control computer for a robot.
negative currents under a positive driving voltage. These os-
cillations may arise due to the interaction within the network
of the spiking components. As the brain also consists of
spiking components and shows emergent mass synchronisa-
tion across certain frequencies (i.e. brainwaves) this result
could show that we are on the right track in attempting to
make neuromorphic (brain-like) computers with memristor
networks. As complex behaviour (and learning) is seen in
other networks of individually ‘simple’ components, such
as Physarum polycephalum, a eukaryotic mould that can
perform simple learning via interaction of its many nuclei,
it suggests that the network structure may be of more
importance than the precise components or measurables.
Regardless of where these brain-wave-like dynamics
emerge from, they have a use regarding time-perception.
These oscillations can be used as an internal clocking signal,
in fact, there is some evidence that this may be part of what
synchronised spiking responses might be used for within the
mammalian brain [11].
IV. DESIGN IMPLICATIONS FOR ROBOTIC
CONTROL SYSTEMS
Let us imagine a robot ‘brain’ built from a complex
memristor network in order to discuss how order and task
switching might be encoded. Consider a standard test of
asking a robot to navigate a T-maze under two different
reward states, namely: I. reaching the left hand top of the
‘T’ cross-bar; II. reaching the right-hand top of the ‘T’ cross-
bar (see [6], [1] as relevant examples). We shall assume that
after training different groups of memristors spike in different
ways for the two solutions (as was seen with artiﬁcial neural
networks in [1]). If the robot was operating under the rule
turn left, we could see that continual brain-wave activity
across the network could be used to keep the memristors
in the correct short-term memory state for the robot to
respond to external stimuli by turning left. Should we switch
the reward state, we would expect the spike patterns to
change (as seen in [1]), causing the memristor network to
switch to the other behaviour. If pre-trained and plastic with
distributed activity (i.e. the cause of the brainwaves) we
can see that this function would allow the whole network
to be switched due to the oscillations across it rather than
waiting for each memristor to switch in turn as the robot
processes the rule change and this may cause the robot to
switch rules faster. This mechanism also allows the robot
brain to have greater plasticity, as previous mechanisms
can be co-opted to encode different responses applicable to
situations outside those the robot has been trained for. Thus,
an artiﬁcial brain based on memristor networks may offer a
time-perception functionality due to the plasticity, learning
and synchronisation properties of the network.
ACKNOWLEDGMENT
E.G. thanks David Howard, Ioannis Georgialas and Oliver
Matthews for helpful discussions.
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