Generalized splay states in phase oscillator networks

Abstract

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

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Cited by in corpus (8)

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• Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
• Multistability and anomalies in oscillator models of lossy power grids
• Stability of rotatory solitary states in Kuramoto networks with inertia
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Dynamics of Minimal Networks of Limit Cycle Oscillators
• Higher-order synchronization on the sphere
• Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling