Abstract
In this paper, a generalized high-dimensional Kuramoto model with directed graphs is investigated. A necessary and sufficient condition for equilibria is given, and the synchronization is proved under weaker directed graph conditions. Firstly, we give some equilibrium criteria under the conditions of strongly connected graphs and even the digraph with a directed spanning tree. Secondly, we weaken the condition of an undirected graph to the case of a directed graph with a directed spanning tree, proving that the generalized high-dimensional Kuramoto model can achieve synchronization. Finally, an example is given to validate the theoretical results.
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