We investigate the critical behavior of the modified Kuramoto model with an asymmetric dynamic interaction which has been proposed to explain the difference between the synchronized frequency and the average intrinsic frequency. We find that the discontinuous phase transition arises when oscillators interact only with other oscillators whose phases are ahead. From the comparison with the conventional Kuramoto model in which the interaction possesses phase reflection symmetry, we conclude that the dynamical symmetry breaking and the dynamic change in interaction structure play important roles in changing the transition nature from continuous to discontinuous ones.

中文翻译：

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不对称动力相互作用的仓本模型中的不连续相变

我们研究了具有不对称动态相互作用的改进的Kuramoto模型的临界行为，该动力学行为已被提出来解释同步频率与平均固有频率之间的差异。我们发现，当振荡器仅与相位超前的其他振荡器相互作用时，就会出现不连续的相变。通过与相互作用具有相反射对称性的传统仓本模型的比较，我们得出结论，动力学对称性的破坏和相互作用结构的动态变化在将过渡性质从连续转变为不连续方面起着重要作用。