Nonuniversal Transitions to Synchrony in the Sakaguchi-Kuramoto Model

We investigate the transition to synchrony in a system of phase oscillators that are globally coupled with a phase lag (Sakaguchi-Kuramoto model). We show that for certain unimodal frequency distributions there appear unusual types of synchronization transitions, where synchrony can decay with increasing coupling, incoherence can regain stability for increasing coupling, or multistability between partially synchronized states and/or the incoherent state can appear. Our method is a bifurcation analysis based on a frequency dependent version of the Ott-Antonsen method and allows for a universal description of possible synchronization transition scenarios for any given distribution of natural frequencies.