  We present a detailed analysis of a model for the synchronization of
nonlinear oscillators due to reactive coupling and nonlinear frequency pulling.
We study the model for the mean field case of all-to-all coupling, deriving
results for the initial onset of synchronization as the coupling or
nonlinearity increase, and conditions for the existence of the completely
synchronized state when all the oscillators evolve with the same frequency.
Explicit results are derived for Lorentzian, triangular, and top-hat
distributions of oscillator frequencies. Numerical simulations are used to
construct complete phase diagrams for these distributions.
