Synchronization dynamics of phase oscillators on power grid models

Max Potratzki; Timo Bröhl; Thorsten Rings; Klaus Lehnertz

doi:10.1063/5.0197930

Synchronization dynamics of phase oscillators on power grid models

Chaos. 2024 Apr 1;34(4):043131. doi: 10.1063/5.0197930.

Authors

Max Potratzki¹, Timo Bröhl^{1

2}, Thorsten Rings^{1

2}, Klaus Lehnertz^{1

2

3}

Affiliations

¹ Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany.
² Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany.
³ Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany.

PMID: 38598675
DOI: 10.1063/5.0197930

Abstract

We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter-a widely used indicator for phase ordering-to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies.