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The synchronization process in a generalized Kuramoto model

In this paper, the critical point that is a coupling strength at which the model changes from desynchronization to synchronization is solved by the mean field method theoretically and the phenomenon that with the increase of the mean value in the Gaussian distribution, the corresponding critical point is reduced is explained. Based on simulation and the theoretical results, the threshold of the mean value at which the model changes from the first order phase transition to the second order phase transition can be predicted and it's found that the threshold is linearly proportional to the variance in the Gaussian distribution.