  The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction
between oscillators is determined by a single harmonic of phase differences of
pairs of oscillators, has very simple emergent dynamics in the case of
identical oscillators that are globally coupled: there is a variational
structure that means the only attractors are full synchrony (in-phase) or splay
phase (rotating wave/full asynchrony) oscillations and the bifurcation between
these states is highly degenerate. Here we show that nonpairwise coupling -
including three and four-way interactions of the oscillator phases - that
appears generically at the next order in normal-form based calculations, can
give rise to complex emergent dynamics in symmetric phase oscillator networks.
In particular, we show that chaos can appear in the smallest possible dimension
of four coupled phase oscillators for a range of parameter values.
