Synchronization of small oscillations

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AUTOMATICA, cilt.107, ss.154-161, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 107
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.automatica.2019.05.047
  • Dergi Adı: AUTOMATICA
  • Sayfa Sayıları: ss.154-161


Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depend on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refinements of this condition for the special cases, where the restorative coupling is either weak or absent, are also presented. (C) 2019 Elsevier Ltd. All rights reserved.