Cycle flows and multistability in oscillatory networks - Kölner UniversitätsPublikationsServer

Manik, Debsankha, Timme, Marc ORCID: 0000-0002-5956-3137 and Witthaut, Dirk ORCID: 0000-0002-3623-5341 (2017). Cycle flows and multistability in oscillatory networks. Chaos, 27 (8). MELVILLE: AMER INST PHYSICS. ISSN 1089-7682

Full text not available from this repository.

DOI:10.1063/1.4994177

Abstract

We study multistability in phase locked states in networks of phase oscillators under both Kuramoto dynamics and swing equation dynamics-a popular model for studying coarse-scale dynamics of an electrical AC power grid. We first establish the existence of geometrically frustrated states in such systems-where although a steady state flow pattern exists, no fixed point exists in the dynamical variables of phases due to geometrical constraints. We then describe the stable fixed points of the system with phase differences along each edge not exceeding pi/2 in terms of cycle flows-constant flows along each simple cycle-as opposed to phase angles or flows. The cycle flow formalism allows us to compute tight upper and lower bounds to the number of fixed points in ring networks. We show that long elementary cycles, strong edge weights, and spatially homogeneous distribution of natural frequencies (for the Kuramoto model) or power injections (for the oscillator model for power grids) cause such networks to have more fixed points. We generalize some of these bounds to arbitrary planar topologies and derive scaling relations in the limit of large capacity and large cycle lengths, which we show to be quite accurate by numerical computation. Finally, we present an algorithm to compute all phase locked states-both stable and unstable-for planar networks. (C) 2017 Author(s).

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Manik, Debsankha	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Timme, Marc	UNSPECIFIED	orcid.org/0000-0002-5956-3137	UNSPECIFIED
Witthaut, Dirk	UNSPECIFIED	orcid.org/0000-0002-3623-5341	UNSPECIFIED