Diversity-induced synchronized oscillations in close-to-threshold excitable elements arranged on regular networks: effects of network topology

TL;DR

This study investigates how network topology affects synchronized oscillations in excitable elements, revealing that shorter average path lengths and lower path length variability enhance synchronization, with local clustering being less influential.

Contribution

It demonstrates the significant impact of global network properties like average path length and path length distribution on synchronization in excitable media.

Findings

Shorter average path length improves synchronization.

Lower standard deviation of path lengths enhances oscillatory behavior.

Local clustering coefficient has less impact on synchronization.

Abstract

The question of how network topology influences emergent synchronized oscillations in excitable media is addressed. Coupled van der Pol-FitzHugh-Nagumo elements arranged either on regular rings or on clusters of the square lattice are investigated. Clustered and declustered rings are constructed to have the same number of next-nearest-neighbors (four) and a number of links twice that of nodes. The systems are chosen to be close-to-threshold, allowing global oscillations to be triggered by a weak diversity among the constituents that, by themselves, would be non-oscillating. The results clearly illustrate the crucial role played by network topology. In particular we found that network performance (oscillatory behavior and synchronization) is mainly determined by the network average path length and by the standard deviation of path lengths. The shorter the average path length and the smaller the standard deviation, the better the network performance. Local properties, as characterized by the clustering coefficient, are less important. In addition we comment on the mechanisms that sustain synchronized oscillations and on the transient times needed to reach these stationary regimes.