Cluster Synchronization of Kuramoto Oscillators Networks

The increasing demand for power makes the synchronization or cluster synchronization of power grid become an essential topic. In this paper, from the view of complex network, the following work is accomplished based on Kuramoto oscillators network: (1) Theoretically prove the condition of frequency cluster synchronization of Kuramoto oscillators network. (2) Using the method of Lagrange multiplier, propose an algorithm to modify the adjacency matrix, which makes a large class of Kuramoto oscillator network reach frequency cluster synchronization after modification. The correctness of the algorithm is verified by numerical simulation. (3) Analyze the stability of the algorithm in (2), we find that the reduction of the number of adjustable adjacency weights will reduce the stability of the algorithm. Besides, the initial value of each oscillator also affects.