Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

TL;DR

This study explores how information transmission delays affect synchronization in scale-free neuronal networks with both attractive and repulsive couplings, revealing delay-induced transitions and regular patterns in neuronal firing.

Contribution

It uncovers the role of delays in synchronization transitions and characterizes delay effects in scale-free neuronal networks with different coupling types.

Findings

Delay influences synchronization, promoting or impairing it.

Regular propagating excitatory fronts depend on oscillation periods.

Minima in synchrony measure occur at specific delay multiples.

Abstract

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.