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For the Kuramoto model and its variations, it is difficult to analyze theexponential synchronization under the general digraphs due to the lack ofsymmetry. %due to the asymmetry of the adjacency matrices. In this paper, forthe high-dimensional Kuramoto model of identical oscillators, a matrix Riccatidifferential equation (MRDE) is proposed to describe the error dynamics. Basedon the MRDE, the exponential synchronization is proved by constructing a totalerror function for the case of digraphs admitting spanning trees. Finally, somenumerical simulations are given to illustrate the obtained theoretical results.

Exponential synchronization of the high-dimensional Kuramoto model with identical oscillators under digraphs