  The Kuramoto model (KM) is a theoretical paradigm for investigating the
emergence of rhythmic activity in large populations of oscillators. A
remarkable example of rhythmogenesis is the feedback loop between excitatory
(E) and inhibitory (I) cells in large neuronal networks. Yet, although the
EI-feedback mechanism plays a central role in the generation of brain
oscillations, it remains unexplored whether the KM has enough biological
realism to describe it. Here we derive a two-population KM that fully accounts
for the onset of EI-based neuronal rhythms and that, as the original KM, is
analytically solvable to a large extent. Our results provide a powerful
theoretical tool for the analysis of large-scale neuronal oscillations.
