On Exponential Synchronization Rates of High-dimensional Kuramoto Models with Identical Oscillators and Digraphs

@article{Peng2022OnES,
  title={On Exponential Synchronization Rates of High-dimensional Kuramoto Models with Identical Oscillators and Digraphs},
  author={Shan Peng and Jinxing Zhang and Jiandong Zhu and Jianquan Lu and Xiaodi Li School of Mathematical Sciences and Nanjing Normal University and Nanjing and China and School of Mathematics and Southeast University and Statistics and Shandong Normal University and Jinan},
  journal={IEEE Transactions on Automatic Control},
  year={2022}
}
For the high-dimensional Kuramoto model with identical oscillators under a general digraph that has a directed spanning tree, although exponential synchronization was proved under some initial state constraints, the exact exponential synchronization rate has not been revealed until now. In this paper, the exponential synchronization rate is precisely determined as the smallest non-zero real part of Laplacian eigenvalues of the digraph. Our obtained result extends the existing results from the… 
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