Generalized splay states in phase oscillator networks

Networks of coupled phase oscillators play an important role in the analysis emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass phase-locked with vanishing mth order parameter. Such typically manifest incoherent dynamics, and they often create high-dimensional families solutions (splay manifolds). For general class oscillator networks, provide explicit linear stability conditions for splay exemplify our results well-known Kuramoto–Sakaguchi model. Importantly, are expressed terms just few observables such as parameter or trace Jacobian. As result, these simple applicable to networks arbitrary size. We generalize findings inertia adaptively models.