  We propose a modification of the Kuramoto model to account for the effective
change in the coupling constant among the oscillators, as suggested by some
experiments on Josephson junction, laser arrays and mechanical systems, where
the active elements are turned on one by one. The resulting model is
analytically tractable and predicts that both first and second order phase
transitions are possible, depending upon the value of a new parameter that
tunes the coupling among the oscillators. Numerical simulations of the model
are in accordance with the analytical estimates, and in qualitative agreement
with the behavior of Josephson junctions coupled via a cavity.

Statistical Mechanics;Disordered Systems and Neural Networks