Stability of entrainment of a continuum of coupled oscillators

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2017-10, Vol.27 (10), p.103108-103108
Main Authors: Snyder, Jordan, Zlotnik, Anatoly, Hagberg, Aric
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Collection
Coupling
Entrainment
Mathematics
MATHEMATICS AND COMPUTING
Oscillators
Resonant frequencies
Stability
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Summary:Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4994567