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The Kuramoto model provides a concrete mathematical realization of emergentsynchrony in a population of phase-coupled oscillators. Since Kuramoto'spublication, \textit{Oscillations, Waves, and Turbulence}, researchers haveworked to better characterize solution dynamics. In this paper, we combine themethod of characteristics with an iterative technique to prove existence anduniqueness of solutions to the continuum version of the Kuramoto model in thespecial case where oscillators are identical and characterize the oscillatordensity in terms of a limiting projected characteristic. The modelcharacterization, in turn, provides for global asymptotic analysis of thesystem via sub and super solutions. We believe the unique approach to modelanalysis developed here has the potential to yield novel results on other morecomplex versions of the extensively studied Kuramoto model.

On solutions to the continuum version of the Kuramoto model with identical oscillators