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We consider the Watts-Strogatz small-world network (SWN) consisting ofinhibitory fast spiking Izhikevich interneurons. This inhibitory neuronalpopulation has adaptive dynamic synaptic strengths governed by the inhibitoryspike-timing-dependent plasticity (iSTDP). In previous works without iSTDP,fast sparsely synchronized rhythms, associated with diverse cognitivefunctions, were found to appear in a range of large noise intensities for fixedstrong synaptic inhibition strengths. Here, we investigate the effect of iSTDPon fast sparse synchronization (FSS) by varying the noise intensity $D$. Weemploy an asymmetric anti-Hebbian time window for the iSTDP update rule [whichis in contrast to the Hebbian time window for the excitatory STDP (eSTDP)].Depending on values of $D$, population-averaged values of saturated synapticinhibition strengths are potentiated [long-term potentiation (LTP)] ordepressed [long-term depression (LTD)] in comparison with the initial meanvalue, and dispersions from the mean values of LTP/LTD are much increased whencompared with the initial dispersion, independently of $D$. In most cases ofLTD where the effect of mean LTD is dominant in comparison with the effect ofdispersion, good FSS (with higher spiking measure) is found to get better viaLTD, 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 tothat in excitatory synaptic plasticity where good (bad) synchronization getsbetter (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibitionstrengths are intensively investigated via a microscopic method based on thedistributions of time delays between the pre- and the post-synaptic spiketimes. Furthermore, we also investigate the effects of network architecture onFSS by changing the rewiring probability $p$ of the SWN in the presence ofiSTDP.

Effect of Inhibitory Spike-Timing-Dependent Plasticity on Fast Sparsely Synchronized Rhythms in A Small-World Neuronal Network