Abstract
The Kuramoto model with time-varying parameters has been extended to consider the effect of delay in couplings. A collective dynamics arises from the interplay between the time scales of the original system, the external forcing, and the delays. This complex low-dimensional dynamics is described, uncovering an echo effect near the synchronization threshold. Hence, the delayed couplings substantially alter the dynamics of what is an open system and should be taken into consideration, depending on the ensemble's evolution time scale. We also introduce a first-harmonic approximation for the evolution of the mean field under harmonic forcing, valid for any delays and forcing of a coherent population.
- Received 30 May 2014
DOI:https://doi.org/10.1103/PhysRevE.90.052903
©2014 American Physical Society