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The effect of phase-lag parameter in pairwise interactions has been a topicof great interest for long. However, real-world systems often have interactionsthat are beyond pairwise and can be modeled using simplicial complexes. Weinvestigate the effect of the inclusion of phase-lag in coupled Kuramotooscillators with simplicial interactions and find that it shifts the criticalpoints at which first-order transition from cluster synchronized state toincoherent state occurs. In the thermodynamic limit, using the Ott-Antonsenapproach we derive a reduced equation for order parameter measuring clustersynchronization. Further, we progress through the self-consistency method toachieve a closed form of the order parameter measuring global synchronizationwhich was lacking in Ott-Antonsen approach. Moreover, considering polarcoordinates framework we obtain rotation frequency of the clusters which comesout to be a function of the phase-lag parameter further indicating thatphase-lag can be used as a control parameter to achieve a desired clusterfrequency.

Rotating synchronized clusters in phase-lagged Kuramoto oscillators with simplicial interactions