  We consider the Watts-Strogatz small-world network (SWN) consisting of
inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal
population has adaptive dynamic synaptic strengths governed by the inhibitory
spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP,
fast sparsely synchronized rhythms, associated with diverse cognitive
functions, were found to appear in a range of large noise intensities for fixed
strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP
on fast sparse synchronization (FSS) by varying the noise intensity $D$. We
employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which
is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)].
Depending on values of $D$, population-averaged values of saturated synaptic
inhibition strengths are potentiated [long-term potentiation (LTP)] or
depressed [long-term depression (LTD)] in comparison with the initial mean
value, and dispersions from the mean values of LTP/LTD are much increased when
compared with the initial dispersion, independently of $D$. In most cases of
LTD where the effect of mean LTD is dominant in comparison with the effect of
dispersion, good FSS (with higher spiking measure) is found to get better via
LTD, while bad FSS (with lower spiking measure) is found to get worse via LTP.
This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to
that in excitatory synaptic plasticity where good (bad) synchronization gets
better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition
strengths are intensively investigated via a microscopic method based on the
distributions of time delays between the pre- and the post-synaptic spike
times. Furthermore, we also investigate the effects of network architecture on
FSS by changing the rewiring probability $p$ of the SWN in the presence of
iSTDP.
