Phase-locked solutions and their stability in the presence of propagation delays |
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Authors: | GAUTAM C SETHIA ABHIJIT SEN FATIHCAN M ATAY |
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Institution: | 1.Institute for Plasma Research,Gandhinagar,India;2.Max Planck Institute for Mathematics in the Sciences,Leipzig,Germany |
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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. |
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