Existence of Partial Entrainment and Stability of Phase Locking Behavior of Coupled Oscillators

摘要: We study a network of all-to-all interconnected phase oscillators as modeled by the Kuramoto model. For coupling strengths larger than critical value, we show existence collective behavior called locking: differences between all are constant in time. As strength increases, distance each pair phases decreases. Stability locking solution is proven for general frequency distributions. There exist one unique asymptotically stable solution. Furthermore description given partial entrainment, which can be regarded finite number analogon synchronization infinite case. When partially entraining some possess an upper and lower bound. Partial entrainment three-cell analyzed: estimate onset proven. Furthermore, local stability with two identical oscillators.