Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization

Details Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization

2009-08-03

arxiv.org/abs/0908.0207v1

Mathematics

Dynamical Systems

11 pages, 2 figures

Scientific paper

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it is shown that the synchronization manifold is semiglobally practically asymptotically stable in the frequency of oscillations.

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