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The Kuramoto model provides a prototypical framework to synchronizationphenomena in interacting particle systems. Apart from full phase synchronywhere all oscillators behave identically, identical Kuramoto oscillators withring-like nonlocal coupling can exhibit more elaborate patterns such asuniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in2006 that the stability of these twisted states depends on the coupling rangeof each oscillator. In this paper, we analyze twisted states and theirbifurcations in the infinite particle limit of ring-like nonlocal coupling. Wenot only consider traditional pairwise interactions as in the Kuramoto modelbut also demonstrate the effects of higher-order nonpairwise interactions,which arise naturally in phase reductions. We elucidate how pairwise andnonpairwise interactions affect the stability of the twisted states, computebifurcating branches, and show that higher-order interactions can stabilizetwisted states that are unstable if the coupling is only pairwise.

Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations