Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings

TL;DR

This study uses a semi-analytical mean-field approach to compare synchronization behaviors in small-world networks of FitzHugh-Nagumo neurons with diffusive versus sigmoid couplings, revealing how coupling type influences synchronization.

Contribution

It provides a detailed comparison of diffusive and sigmoid couplings in small-world neural networks using a semi-analytical method, highlighting the role of coupling type in synchronization.

Findings

Weak heterogeneity slightly increases synchronization with diffusive couplings.

Synchronization decreases with sigmoid couplings when heterogeneity is introduced.

Diffusive couplings enhance synchronization due to local negative feedback, not network structure.

Abstract

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity between results for {\it diffusive} and {\it sigmoid} couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but not due to the shorten average distance in SW networks. Synchronization of SW networks depends not only on their structure but also on the type of couplings.