  Memristors have uses as artificial synapses and perform well in this role in
simulations with artificial spiking neurons. Our experiments show that
memristor networks natively spike and can exhibit emergent oscillations and
bursting spikes. Networks of near-ideal memristors exhibit behaviour similar to
a single memristor and combine in circuits like resistors do. Spiking is more
likely when filamentary memristors are used or the circuits have a higher
degree of compositional complexity (i.e. a larger number of anti-series or
anti-parallel interactions). 3-memristor circuits with the same memristor
polarity (low compositional complexity) are stabilised and do not show spiking
behaviour. 3-memristor circuits with anti-series and/or anti-parallel
compositions show richer and more complex dynamics than 2-memristor spiking
circuits. We show that the complexity of these dynamics can be quantified by
calculating (using partial auto-correlation functions) the minimum order
auto-regression function that could fit it. We propose that these oscillations
and spikes may be similar phenomena to brainwaves and neural spike trains and
suggest that these behaviours can be used to perform neuromorphic computation.
