Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions

Abstract: Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott--Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is $\pi$ apart) as well as twisted states with a different winding number.