Stability of phase locking and existence of entrainment in networks of globally coupled oscillators

Abstract We study a network of a finite number of all-to-all interconnected phase oscillators as modeled by the Kuramoto model. For coupling strengths larger than a critical value, we show the existence of a collective behavior called phase locking: the phase differences between all oscillators are constant in time. Stability of each phase locking solution is proven for general frequency distributions. Furthermore a description is given of partial entrainment: some but not all phase differences remain bounded. For the three cell network an estimation of the coupling strength at the onset of partial entrainment is computed.