Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder
Abstract
Active rotator models provide a minimal phase description of excitable and oscillatory systems and have long been used to study mutual entrainment, synchronization, and collective transitions. In this paper, we investigate fully connected active rotator networks with Kuramoto coupling, where a common positive intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. We characterize the dynamics using the mean absolute late-time drift, the polar and nematic order parameters, and the fractions of positive and negative drifting oscillators. The model with an even mixed-sign feedback ensemble has an exact discrete symmetry under a simultaneous phase shift by π and reversal of the feedback amplitudes. This exposes two physically distinct low-drift states: at weak coupling and strong disorder, local pinning produces an approximately antipodal, nematically ordered population, whereas at strong coupling the system can form a polar, coherently pinned state. A self-consistent stationary mean-field theory determines the existence edge of a nonzero coherent branch, provides quantitative predictions for the polar and nematic order, and shows that the coherent branch followed here is fully pinned. Sustained negative drift is impossible in a stationary mean field; the negative-drift population observed is instead localized to an intermediate-coupling regime characterized by a non-stationary mean field. Finally, finite-size extrapolations show persistent coupling-induced drift recovery and are compatible with vanishing strong-coupling drift at large disorder in the thermodynamic limit. These results show that even with a homogeneous intrinsic drive, mixed-sign local feedback can generate distinct regimes of drift, pinning, and collective phase organization.
Related
- Inferring Coupling Strength from the Kuramoto Order Parameter
- Transfer Dynamics and Spectral Cascades in Graph-Coupled Kuramoto Networks
- Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure
- Beyond 11/16: dense Kuramoto networks that resist synchrony
- Multistability and Juggling States in Frustrated Kuramoto Oscillators on Ring Networks
BibTeX
@misc{dey2026collective,
title = {{Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder}},
author = {Arpan Dey},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10032},
eprint = {2606.10032},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05785270v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder
AU - Arpan Dey
PY - 2026
DA - 2026/09/10
PB - HAL
DO - 10.48550/arxiv.2606.10032
UR - https://hal.science/hal-05785270v1
AB - Active rotator models provide a minimal phase description of excitable and oscillatory systems and have long been used to study mutual entrainment, synchronization, and collective transitions. In this paper, we investigate fully connected active rotator networks with Kuramoto coupling, where a common positive intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. We characterize the dynamics using the mean absolute late-time drift, the polar and nematic order parameters, and the fractions of positive and negative drifting oscillators. The model with an even mixed-sign feedback ensemble has an exact discrete symmetry under a simultaneous phase shift by π and reversal of the feedback amplitudes. This exposes two physically distinct low-drift states: at weak coupling and strong disorder, local pinning produces an approximately antipodal, nematically ordered population, whereas at strong coupling the system can form a polar, coherently pinned state. A self-consistent stationary mean-field theory determines the existence edge of a nonzero coherent branch, provides quantitative predictions for the polar and nematic order, and shows that the coherent branch followed here is fully pinned. Sustained negative drift is impossible in a stationary mean field; the negative-drift population observed is instead localized to an intermediate-coupling regime characterized by a non-stationary mean field. Finally, finite-size extrapolations show persistent coupling-induced drift recovery and are compatible with vanishing strong-coupling drift at large disorder in the thermodynamic limit. These results show that even with a homogeneous intrinsic drive, mixed-sign local feedback can generate distinct regimes of drift, pinning, and collective phase organization.
ER -