The new energy source is connected to the grid through the inverter, and the voltage amplitude, phase, frequency and other physical quantities of the grid-connected inverter system have strong interactive coupling in electromagnetic, electromechanical and other time scales. It is a hot issue to accurately grasp the dominant behavior characteristics of synchronous stability of grid-connected inverters. Therefore, a multiple density-based spatial clustering of applications with noise (DBSCAN) algorithm is proposed to analyze the physical characterization of the synchronous stability of grid-connected multi-inverter systems. Firstly, the grid-connected models of grid-following inverters and grid-forming inverters are established, and the synchronization characteristics of their synchronous control units are analyzed. Secondly, the proposed algorithm is used to cluster and classify simulation data of the phase difference between the grid-connected inverter and the common connection point, the inverter power angle, the system frequency and so on. Finally, the simulation analysis shows that the power angle of the grid-connected inverter system is gradually restored to the original operating state and the new steady state. In addition, the system synchronization stability is consistent with the frequency stability. The successful phase locking of the grid-following inverters synchronous control unit can characterize the synchronization stability of the system, while the grid-forming inverters synchronous control unit cannot.