We study the synchronization critical coupling in the Kuramoto model of globally coupled oscillators, analyzing natural frequencies distributed according to unimodal functions. Its is shown that asymmetric distributions can lead to a nonmonotonic critical transition when we modify some of their parameters. In particular, we explore the case in which the natural frequencies are given by the log-normal distribution. This case presents an interesting behavior in which synchrony vanishes with the increase in dispersion of natural frequencies, but the continuous increase in dispersion may also recover part of the synchronization. Our numerical results are compared with analytical predictions based on self-consistent equations.

我们在全局耦合振荡器的Kuramoto模型中研究了同步临界耦合，分析了根据单峰函数分布的固有频率。结果表明，当我们修改某些参数时，不对称分布会导致非单调临界转变。特别是，我们探讨了自然频率由对数正态分布给出的情况。这种情况表现出一种有趣的行为，其中同步随着自然频率的色散增加而消失，但是色散的连续增加也可以恢复部分同步。我们将数值结果与基于自洽方程的分析预测进行比较。