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

Gautam C. Sethia, Abhijit Sen, and Fatihcan M. Atay

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Submission date: 11. May. 2010
published in: Physical review / E, 81 (2010) 5, art-no. 056213 
DOI number (of the published article): 10.1103/PhysRevE.81.056213
Bibtex
PACS-Numbers: 05.45.Ra, 05.45.Xt, 89.75.-k
Keywords and phrases: distance-dependent delay, phase oscillator, synchronization

Abstract:
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.