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    • Phase-locked solutions and their stability in the presence of propagation delays

      Gautham C Sethia Abhijit Sen Fatihcan M Atay

      Synchronization, Coupled Systems and Networks Volume 77 Issue 5 November 2011 pp 905-915

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      https://www.ias.ac.in/article/fulltext/pram/077/05/0905-0915

    • Keywords

       

      Synchronization; propagation delays; nonlocal coupling; phase oscillators; marginal stability curve.

    • Abstract

       

      We investigate phase-locked solutions of a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and travelling wave solutions in the parameter space characterizing the nonlocality and time delay are delineated. For the synchronous states a comprehensive stability diagram is presented that provides a heuristic synchronization condition as well as an analytic relation for the marginal stability curve. The relation yields simple stability expressions in the limiting cases of local and global coupling of phase oscillators.

    • Author Affiliations

       

      Gautham C Sethia1 Abhijit Sen1 Fatihcan M Atay2

      1. Institute for Plasma Research, Bhat, Gandhinagar 382 428, India
      2. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, Leipzig D-04103, Germany

    • Dates

       
      Published
      November 2011

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