title: Homogeneous delays in the Kuramoto model with time-variable parameters.
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.
authors.affiliation: Department of Theoretical Physics and Astrophysics, Physics Faculty, Belarusian State University, Nezavisimosty Av., 4, 220030, Minsk, Belarus.
authors.forename: Miraslau L
authors.initials: ML
authors.lastname: Barabash
authors.affiliation: Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
authors.forename: Spase
authors.initials: S
authors.lastname: Petkoski
authors.affiliation: Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
authors.forename: Aneta
authors.initials: A
authors.lastname: Stefanovska