  We consider clustered small-world networks with both inhibitory (I) and
excitatory (E) populations. This I-E neuronal network has adaptive dynamic I to
E and E to I interpopulation synaptic strengths, governed by interpopulation
spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast
sparsely synchronized rhythms, related to diverse cognitive functions, were
found to appear in a range of noise intensity $D$ for static synaptic
strengths. By varying $D$, we investigate the effect of interpopulation STDPs
on diverse population and individual properties of fast sparsely synchronized
rhythms that emerge in both the I- and the E-populations. Depending on values
of $D$, long-term potentiation (LTP) and long-term depression (LTD) for
population-averaged values of saturated interpopulation synaptic strengths are
found to occur, and they make effects on the degree of fast sparse
synchronization. In a broad region of intermediate $D$, the degree of good
synchronization (with higher spiking measure) becomes decreased, while in a
region of large $D$, the degree of bad synchronization (with lower spiking
measure) gets increased. Consequently, in each I- or E-population, the
synchronization degree becomes nearly the same in a wide range of $D$. This
kind of "equalization effect" is found to occur via cooperative interplay
between the average occupation and pacing degrees of fast sparsely synchronized
rhythms. We note that the equalization effect in interpopulation synaptic
plasticity is distinctly in contrast to the Matthew (bipolarization) effect in
intrapopulation (I to I and E to E) synaptic plasticity where good (bad)
synchronization gets better (worse). Finally, emergences of LTP and LTD of
interpopulation synaptic strengths are intensively investigated via a
microscopic method based on the distributions of time delays between the pre-
and the post-synaptic spike times.
