Collective excitability in highly diluted networks of rotators

TL;DR

This paper demonstrates that highly diluted random networks of rotators can exhibit collective excitable events driven by local adaptation, showing robustness of these phenomena across different models and network dilutions.

Contribution

It reveals the emergence of collective excitability in highly diluted networks of rotators through a self-sustained adaptation mechanism, extending understanding beyond fully-coupled systems.

Findings

Collective excitability persists despite network dilution.

System response varies with stimulation protocols and dilution levels.

Phenomena are robust across different Kuramoto models.

Abstract

We report on collective excitable events in a highly-diluted random network of non-excitable nodes. Excitability arises thanks to a self-sustained local adaptation mechanism that drives the system on a slow time-scale across a hysteretic phase transition involving states with different degrees of synchronization. These phenomena have been investigated for the Kuramoto model with bimodal distribution of the natural frequencies and for the Kuramoto model with inertia and an unimodal frequency distribution. We consider global and local stimulation protocols and characterize the system response for different level of dilution. We compare the results with those obtained in the fully-coupled case showing that such collective phenomena are remarkably robust against network diluteness.