Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an
ensemble of coupled excitable rotators. We find that a moderate
fraction of repulsive interactions can trigger global firing of the
ensemble. The regime of global firing, however, is suppressed in
sufficiently large systems if the network of repulsive interactions
is fully random, due to self-averaging in its degree distribution.
We thus introduce a model of partially random networks with a broad
degree distribution, where self-averaging due to size growth is
absent. In this case, the regime of global firing persists for large
sizes. Our results extend previous work on the constructive effects
of diversity in the collective dynamics of complex systems