Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks
Dynamical Systems
2016-02-10 v2
Abstract
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptotic stability of the synchronization subspace and the second smallest eigenvalue of the Laplacian matrix.
Keywords
Cite
@article{arxiv.1507.08428,
title = {Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks},
author = {S. Emre Tuna},
journal= {arXiv preprint arXiv:1507.08428},
year = {2016}
}
Comments
13 pages, 8 figures