article · 01/01/2017
Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales
Résumé
We identify the breaking of time-translation invariance in a deterministic system of repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. We analyze random and regular implementations of frequency distributions and consider grid sizes with different characteristics of the attractor space, which is by construction quite rich. This may cause long transients until the deterministic trajectories find their stationary orbits. The stationary orbits are limit cycles with periods that extend over orders of magnitude. It is the long transient times that cause the breaking of time-translation invariance in autocorrelation functions of oscillator phases. This feature disappears close to the transition to the monostable phase, where the phase trajectories are just irregular and no stationary behavior can be identified. Copyright (C) EPLA, 2017
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Esmaeili, S., Labavic, D., Pleimling, M., & Meyer-Ortmanns, H. (2017). Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales. EPL, 118(4). https://doi.org/10.1209/0295-5075/118/40006@article{Esmaeili2017_356,
author = {Esmaeili, Shadisadat and Labavic, Darka and Pleimling, Michel and Meyer-Ortmanns, Hildegard},
year = {2017},
month = {1},
title = {Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales},
journal = {EPL},
publisher = {IOP PUBLISHING LTD},
volume = {118},
number = {4},
address = {TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND},
abstract = {We identify the breaking of time-translation invariance in a deterministic system of repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. We analyze random and regular implementations of frequency distributions and consider grid sizes with different characteristics of the attractor space, which is by construction quite rich. This may cause long transients until the deterministic trajectories find their stationary orbits. The stationary orbits are limit cycles with periods that extend over orders of magnitude. It is the long transient times that cause the breaking of time-translation invariance in autocorrelation functions of oscillator phases. This feature disappears close to the transition to the monostable phase, where the phase trajectories are just irregular and no stationary behavior can be identified. Copyright (C) EPLA, 2017},
url = {http://www.dx.doi.org/10.1209/0295-5075/118/40006},
doi = {10.1209/0295-5075/118/40006},
issn = {0295-5075},
}TY - JOUR
AU - Esmaeili, Shadisadat
AU - Labavic, Darka
AU - Pleimling, Michel
AU - Meyer-Ortmanns, Hildegard
PY - 2017
DA - 2017/01/01
TI - Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales
JO - EPL
VL - 118
IS - 4
PB - IOP PUBLISHING LTD
SN - 0295-5075
AB - We identify the breaking of time-translation invariance in a deterministic system of repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. We analyze random and regular implementations of frequency distributions and consider grid sizes with different characteristics of the attractor space, which is by construction quite rich. This may cause long transients until the deterministic trajectories find their stationary orbits. The stationary orbits are limit cycles with periods that extend over orders of magnitude. It is the long transient times that cause the breaking of time-translation invariance in autocorrelation functions of oscillator phases. This feature disappears close to the transition to the monostable phase, where the phase trajectories are just irregular and no stationary behavior can be identified. Copyright (C) EPLA, 2017
DO - 10.1209/0295-5075/118/40006
UR - http://www.dx.doi.org/10.1209/0295-5075/118/40006
ER -