Three-body interactions with time delay.

This work focuses on the dynamics of globally coupled phase oscillators with three-body interaction and time delay. Analytic estimates regarding the stability of the incoherent solution are presented. Expressions for the phase synchronization frequencies and their stability are also derived. These theoretical results are supplemented with appropriate numerical computations. Numerical results regarding the fluctuations observed in the synchronization order parameter are then discussed. Some comparative results for phase synchronization in two-body, three-body, and mixed-coupled systems for different coupling combinations are also presented.