Dynamical Phase transitions in Kuramoto model with distributed Sakaguchi phase

Abstract: In this numerical work we have systematically studied the dynamical phase transitions in the Kuramoto- Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the numerical steady state phase diagrams for quenched and annealed kinds of disorder in the Sakaguchi parameters using the conventional order parameter and other statistical quantities like strength of incoherence and discontinuity measures. We have also considered the correlation profile of the local order parameter fluctuations in the various identified phases. The phase diagrams for quenched disorder is qualitatively much different than those the global coupling regime. The order of various transitions are confirmed by a study of the distribution of the order parameter and its fourth order Binder cumulant across the transition for an ensemble of initial distribution of phases. For annealed type of disorder, in contrast to the case with the quenched disorder, the system is almost insensitive to the amount of disorder. We also elucidate the role of chimeralike states in the synchronizing transition of the system and study the effect of disorder on these states. Finally, we seek justification of our results from simulations guided by the Ott-Antonsen ansatz.