English

Synchronization of linear oscillators coupled through dynamic networks with interior nodes

Dynamical Systems 2019-06-21 v1

Abstract

Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix representing the coupling has a single eigenvalue on the imaginary axis.

Keywords

Cite

@article{arxiv.1906.08572,
  title  = {Synchronization of linear oscillators coupled through dynamic networks with interior nodes},
  author = {S. Emre Tuna},
  journal= {arXiv preprint arXiv:1906.08572},
  year   = {2019}
}

Comments

11 pages, 4 figures

R2 v1 2026-06-23T09:58:54.648Z