November 03, 2012

Observation of Spontaneous Bursting Spike Patterns Simple Three Memristor Circuits

Arxiv - The memristor is the fourth fundamental circuit element which was predicted to exist from symmetry arguments in 1971. It is a two terminal passive device. It is stateful and the internal state is related to past history of the device. Because of the memristor's ability to learn it has been proposed that the memristor could be a route to neuromorphic or brain-like hardware. As the achievement of this is widely anticipated to lead to a step-change in not just computing, but science and even society itself (if it works we would be able to make a true machine intelligence which could enable us to answer fascinating philosophical questions about the nature of consciousness, intelligence and mankind).

The distinctive switching spikes seen in single memristor circuits can be suppressed in networks of memristors. Instead oscillatory behaviour interrupted by spontaneous irregular bursting spike patterns are observed. An investigation of two and three memistor circuits was undertaken to elucidate the origin and nature of these rich dynamics. No spiking or oscillations are seen in circuits where all the memristors are arranged with matching polarity. Spiking is seen in circuits where memristors are arranged anti-parallel. These dynamics may be due to increased sensitivity to initial conditions or deterministic chaos and are potentially useful for neuromorphic computing.

We have shown that three memristors can produce rich behaviour, including
brain-wave-like oscillations and spiking events. An interesting question is where
has the large spike at the start gone and where have the switching spikes ex-
pected from the I-V curve gone. We believe that the energy of the current spike,
in fact the current itself, has been `absorbed' into the memristor network and
is the cause of the latter spiking events

We have shown that for two or three memristors that are very similar to each other and wired up with the same polarity, Chua's prediction that they would behave exactly like a single memristor is true. We have also shown that when there is either parallel interaction or a polarity diff erence between the memristors, there is a higher chance of richer behaviour. From these circuits it is apparent that the circuit fragment of two memristors in antiparallel (i.e in parallel with opposite polarity) has the highest chance of neuromorphic-like rich dynamics. This is supported by the results reported in the literature and suggests that the theoretical results reported in are due to the fact their Chua circuit possesses two memristors in anti-parallel rather than a problem with the model.

The background oscillations are interesting. Although they could be dismissed as sampling noise or background noise, we do not believe this to be the case as they are not seen in the single memristor circuit and are several orders of magnitude above what would be expected on the experimental set-up used. They could be some low level emergent phenomena related to the spikes. In- stead, we think it's to do with the movement of the boundary, w(t). These `waves' appear similar to that of interacting oscillators, and thus we think its potentially related to the boundary which may be oscillating due to the movement of ions around the dynamic equilibrium point, and it is this behaviour that adds up and interacts in the circuit with more than one memristor in it.

This letter represents preliminary work in this area. Although the dynamics look rich, we need to do further analysis to discover what is the cause of this behavioural richness, quantify it and test whether the trajectory is genuinely chaotic. We are currently undertaking further investigations, both experimental and theoretical, into the mechanism of this behaviour.

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