# Dynamical Phase transitions in Kuramoto model with distributed Sakaguchi phase

## TL;DR

This study investigates how disorder in Sakaguchi phases affects dynamical phase transitions in the Kuramoto model, revealing distinct behaviors for quenched and annealed disorder and highlighting the role of chimeralike states.

## Contribution

It provides a comprehensive numerical analysis of phase diagrams and transition orders in the Kuramoto-Sakaguchi model with different disorder types, supported by Ott-Antonsen ansatz simulations.

## Key findings

- Quenched disorder leads to qualitatively different phase diagrams than global coupling.
- Transition orders are confirmed via Binder cumulant analysis.
- System is insensitive to disorder in the annealed case.

## 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.