The effect of distributed time-delays on the synchronization of neuronal networks

TL;DR

This study examines how distributed time delays in neuronal network coupling influence synchronization, finding that such delays do not significantly alter the synchronization transition compared to constant delays, across various network topologies.

Contribution

It demonstrates that distributed delays have minimal impact on synchronization, supporting the relevance of constant delay models in realistic neuronal networks.

Findings

Distributed delays do not significantly change synchronization behavior.

Normal delay distribution lowers the coupling threshold for transition.

Results are consistent across different network topologies.

Abstract

Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the distributed delays. We also notice that a normal distribution of delays gives rise to a transition at marginally lower coupling strengths, vis-a-vis uniformly distributed delays. These trends hold across classes of networks and for varying standard deviations of the delay distribution, indicating the generality of these results. So we conclude that distributed delays, which may be typically expected in real-world situations, do not have a notable effect on synchronization. This allows results obtained with constant delays to remain relevant even in the case of randomly distributed delays.