Synchronization of small oscillations

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2019-09-01

Author

Tuna, Sezai Emre

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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.

Subject Keywords

Control and Systems Engineering, Electrical and Electronic Engineering

URI

https://hdl.handle.net/11511/49241

Journal

AUTOMATICA

DOI

https://doi.org/10.1016/j.automatica.2019.05.047

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Department of Electrical and Electronics Engineering, Article

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Citation Formats

S. E. Tuna, “Synchronization of small oscillations,” AUTOMATICA, pp. 154–161, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49241.