Robustness of synchronizability in windmill networks with node failures

In this paper, the synchronizability characterized by the Laplacian spectrum is applied to windmill networks where three types of parameters are introduced to control the number of deleted nodes. Using the network's structures, exact solutions of the Laplacian eigenvalues are obtained and metrics of the synchronizability are correspondingly shown. Relationships between the synchronizability and the introduced parameters are presented. Then, the synchronizability of models with different settings of node failures is compared. The obtained results reveal distinct synchronizabilities originating from intrinsic structures of models and the setting forms of node failures. Finally, numerical examples are provided to verify the effectiveness of theoretical analysis.