Harmonic synchronization under all three types of coupling: Position, velocity, and acceleration


Automatica, vol.130, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 130
  • Publication Date: 2021
  • Doi Number: 10.1016/j.automatica.2021.109727
  • Title of Journal : Automatica
  • Keywords: Synchronization, Laplacian matrix, Harmonic oscillator, Acceleration coupling, OSCILLATORS, NETWORK


© 2021 Elsevier LtdSynchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.