# Stochastic Spike Synchronization in A Small-World Neural Network with Spike-Timing-Dependent Plasticity

## TL;DR

This paper studies how spike-timing-dependent plasticity influences stochastic spike synchronization in a small-world neural network, revealing a positive feedback mechanism that enhances or diminishes synchronization based on initial conditions.

## Contribution

It introduces the impact of additive and multiplicative STDP on noise-induced spike synchronization in small-world networks, highlighting the Matthew effect in synaptic plasticity.

## Key findings

- Additive STDP causes a Matthew effect in synchronization.
- LTP enhances good synchronization, LTD worsens poor synchronization.
- Microscopic analysis links spike timing distributions to synaptic strength changes.

## Abstract

We consider the Watts-Strogatz small-world network consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities through competition between the constructive and the destructive roles of noise. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation (LTP) of synaptic strengths, while bad synchronization gets worse via long-term depression (LTD). Emergence of LTP and LTD of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on the states) on the SSS are also studied and discussed in comparison with the case of additive STDP.