Abstract: Firstly, the influence of the structure of the star network on synchronization was discussed by using the theory of rotating periodic solutions. The existence of various types of synchronization solutions in star networks was judged, and  the relationship between symmetry of the star network and synchronization solutions was given. Secondly, in the star network, all the rotating matrices satisfying the rotating periodic conditions formed some special groups. By using the conjugate classes of these groups and diagonalization method, we obtained various  types of synchronization solutions.

Key words: star network, synchronization, rotating periodic solution, group, conjugate class