Abstract: We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry and phase lags. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction, where the first and second harmonic interactions with phase lags naturally appear. Our study indicates that the higher-order interactions induce anomalous transitions to synchrony. Unlike the conventional Kuramoto model, higher-order interactions lead to anomalous phenomena such as multistability of full synchronization, incoherent, and two-cluster states, and transitions to synchrony through slow switching and clustering. Phase diagrams of the dynamical regimes are constructed theoretically and verified by direct numerical simulations. We also show that similar transition scenarios are observed even if a small heterogeneity in the oscillators' frequency is included.

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