Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays

We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results a heuristic...

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Bibliographic Details
Published in:arXiv.org 2010-05
Main Authors: Sethia, Gautam C, Sen, Abhijit, Atay, Fatihcan M
Format: Article
Language:English
Subjects:
Oscillators
Parameters
Propagation
Stability analysis
Synchronism
Online Access:Get full text
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Summary:We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results a heuristic synchronization condition is suggested, and an analytic relation for the marginal stability curve is obtained. We also provide an expression in the form of a scaling relation that closely follows the marginal stability curve over the complete range of the non-locality parameter.
ISSN:2331-8422
DOI:10.48550/arxiv.1003.5079