Connectivity-disorder effect on collective synchronization

We investigate a system of random frequency oscillators coupled through sparse random networks and explore connectivity-disorder effects on collective synchronization. In particular, we pay attention to how the random quenched disorder in connectivity affects the nature of synchronization transitions. The oscillator frequencies are assigned independently from an unimodal, bimodal, or uniform distribution. Extensive numerical simulations as well as the mean-field analysis have been performed on Erd{\"o}s-R{\'e}nyi random networks. We find that the quenched connectivity disorder invalidates the mean-field prediction of distinctive transition natures depending on frequency distributions in random networks. In fact, the same continuous synchronization transition is found for all types of frequency distributions. The physical origin of this unexpected result is discussed.