The effect of phase-lag in pairwise interactions has been a topic of great interest for a while. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We show that the inclusion of higher-order interactions in phase-lagged coupled Kuramoto oscillators shifts the critical point at which first-order transition from a cluster synchronized state to an incoherent state takes place. Considering the polar coordinates, we obtain the rotation frequency of the clusters, which turns out to be a function of the phase-lag parameter. In turn, the phase- lag can be used as a control parameter to achieve a desired cluster frequency. Moreover, in the thermodynamic limit, by employing the Ott-Antonsen approach we derive a reduced equation for the order parameter measuring cluster synchronization and progress further through the self-consistency method to obtain a closed form of the order parameter measuring global synchronization which was lacking in the Ott-Antonsen approach.

中文翻译：

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具有高阶相互作用的相位滞后 Kuramoto 振荡器中的旋转簇

成对相互作用中相位滞后的影响一段时间以来一直是人们非常感兴趣的话题。然而，现实世界的系统通常具有超出成对范围的交互作用，并且可以使用单纯复形进行建模。我们表明，相位滞后耦合仓本振荡器中包含高阶相互作用会改变从簇同步状态到非相干状态的一阶转变发生的临界点。考虑到极坐标，我们获得了簇的旋转频率，它是相位滞后参数的函数。反过来，相位滞后可以用作控制参数以实现期望的集群频率。此外，在热力学极限下，通过采用Ott-Antonsen方法，我们推导了测量簇同步的序参数的简化方程，并进一步通过自洽方法获得了测量全局同步的序参数的闭合形式，这是缺乏的在奥特-安东森方法中。