Synchronization transitions in delay-coupled phase oscillator networks with higher-order interactions

This study investigates the synchronization transitions in networks of phase oscillators connected through time delays in higher-order structure. Also, a direct numerical approach that retains the full complexity of the oscillator dynamics is considered. The model incorporates equal time delays across all coupling terms and includes pairwise, 2-simplex, and 3-simplex interactions. The study analyzes how synchronization evolves under varying coupling strengths, with particular attention to the synchronization transition, whether continuous or explosive. Using Lorentzian and uniform natural frequency distributions shows that delay and interaction order significantly influence the system’s dynamics. Also, higher-order interactions in the presence of delay trigger hysteresis and abrupt phase transitions. These results provide insight into collective behavior and real-world systems where delay and group interactions exist, such as power grids and neural communication networks.