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Generalized splay states in phase oscillator networks

Berner, Rico; Yanchuk, Serhiy; Maistrenko, Yuri; Schöll, Eckehard

FG Nichtlineare Dynamik und Kontrolle

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 mth 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. Published under an exclusive license by AIP Publishing.
  • This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in: Berner, R., Yanchuk, S., Maistrenko, Y., & Schöll, E. (2021). Generalized splay states in phase oscillator networks. In Chaos: An Interdisciplinary Journal of Nonlinear Science (Vol. 31, Issue 7, p. 073128). AIP Publishing. https://doi.org/10.1063/5.0056664 and may be found at https://doi.org/10.1063/5.0056664.