Delay-induced multistability in one-dimensional swarmalators with common intrinsic frequency
Abstract
We study the delayed one-dimensional swarmalator model when all units share a common intrinsic frequency ω. Unlike the zero-frequency case, ω cannot be removed by a rotating-frame transformation because delayed interactions retain the phase accumulated over the lag. The result is a two-order-parameter analogue of the delayed Kuramoto model: the asynchronous state acquires incoherence lobes, the synchronized state becomes a rotating branch stable even when both the spatial and phase couplings are repulsive, and the phase wave develops narrow resonant stability bands. These delay-selected windows overlap to produce broad branch coexistence, including a narrow window near K=-J where all three canonical states-asynchronous, phase wave, and synchronized-are simultaneously stable. In regions where no canonical branch is stable, the order parameters oscillate persistently.
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BibTeX
@misc{djeudjo2026delayinduced,
title = {{Delay-induced multistability in one-dimensional swarmalators with common intrinsic frequency}},
author = {Rommel Tchinda Djeudjo and Timoteo Carletti and Kevin P. O'Keeffe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36293},
eprint = {2609.36293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36293},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Delay-induced multistability in one-dimensional swarmalators with common intrinsic frequency
AU - Rommel Tchinda Djeudjo
AU - Timoteo Carletti
AU - Kevin P. O'Keeffe
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36293
UR - https://arxiv.org/abs/2609.36293
AB - We study the delayed one-dimensional swarmalator model when all units share a common intrinsic frequency ω. Unlike the zero-frequency case, ω cannot be removed by a rotating-frame transformation because delayed interactions retain the phase accumulated over the lag. The result is a two-order-parameter analogue of the delayed Kuramoto model: the asynchronous state acquires incoherence lobes, the synchronized state becomes a rotating branch stable even when both the spatial and phase couplings are repulsive, and the phase wave develops narrow resonant stability bands. These delay-selected windows overlap to produce broad branch coexistence, including a narrow window near K=-J where all three canonical states-asynchronous, phase wave, and synchronized-are simultaneously stable. In regions where no canonical branch is stable, the order parameters oscillate persistently.
ER -