Irregular macroscopic dynamics due to chimera states in small-world networks of pulse-coupled oscillators

We study the collective dynamics of excitatory integrate-and-fire-like oscillators interacting via δ -pulses on a small-world network. The oscillators are endowed with refractory periods and time delays. For weak coupling strengths, the network self-organizes into synchronous and asynchronous regions. Such chimera states allow for two separate routes to synchrony/asynchrony. In addition to the loss of stability of either synchronous or asynchronous regions mediated by long-ranged connections, regions may grow or shrink mediated by the lattice structure. The interplay between these behaviors leads to controlled total sizes of asynchronous regions or to an alternation of synchronization and desynchronization phenomena with irregular macroscopic observables.