  The Bienenstock-Cooper-Munro (BCM) and Spike Timing-Dependent Plasticity
(STDP) rules are two experimentally verified form of synaptic plasticity where
the alteration of synaptic weight depends upon the rate and the timing of pre-
and post-synaptic firing of action potentials, respectively. Previous studies
have reported that under specific conditions, i.e. when a random train of
Poissonian distributed spikes are used as inputs, and weight changes occur
according to STDP, it has been shown that the BCM rule is an emergent property.
Here, the applied STDP rule can be either classical pair-based STDP rule, or
the more powerful triplet-based STDP rule. In this paper, we demonstrate the
use of two distinct VLSI circuit implementations of STDP to examine whether BCM
learning is an emergent property of STDP. These circuits are stimulated with
random Poissonian spike trains. The first circuit implements the classical
pair-based STDP, while the second circuit realizes a previously described
triplet-based STDP rule. These two circuits are simulated using 0.35 um CMOS
standard model in HSpice simulator. Simulation results demonstrate that the
proposed triplet-based STDP circuit significantly produces the threshold-based
behaviour of the BCM. Also, the results testify to similar behaviour for the
VLSI circuit for pair-based STDP in generating the BCM.
