Effect of diversity distribution symmetry on global oscillations of networks of excitable units

We show that the degree of symmetry of the diversity distribution is the key determinant of global oscillations in coupled networks of FitzHugh-Nagumo units, used as prototypical examples of excitable systems. In these ensembles, symmetric diversity reliably yields resonant collective oscillations-even when all units are individually excitable-whereas asymmetric diversity suppresses them. Two symmetry-based metrics predict the presence or absence of global oscillations from the distribution alone. A simple mean-field mechanism, corroborated by a minimal two-unit analysis, explains how symmetry creates a landscape that supports limit cycles. These results identify diversity distribution symmetry as a key mechanism for emergent synchronization in excitable media.