Delay-induced multirhythmicity in a 3-cell inhibitory network
Abstract
We study the dynamics of a delayed three-cell central pattern generator network using return-map analysis and a phase-reduced description derived from generalized FitzHugh-Nagumo oscillators. The phase model captures the emergence and stability of synchronous, pacemaker, and traveling-wave rhythms and provides a systematic, computationally efficient framework for characterizing the network dynamics beyond direct return-map calculations. We conduct extensive two-parameter analyses of both the full and phase-reduced models, revealing rich multi-rhythmic dynamics and transitions among coexisting rhythmic states. The close agreement between the two descriptions establishes phase reduction as an efficient and reliable framework for characterizing the dynamical organization of delayed neural oscillator networks.
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BibTeX
@misc{qie2026delayinduced,
title = {{Delay-induced multirhythmicity in a 3-cell inhibitory network}},
author = {Xinxin Qie and Morten Gram Pedersen and Jian Song and Shenquan Liu and Andrey L. Shilnikov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06836},
eprint = {2611.06836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06836},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Delay-induced multirhythmicity in a 3-cell inhibitory network
AU - Xinxin Qie
AU - Morten Gram Pedersen
AU - Jian Song
AU - Shenquan Liu
AU - Andrey L. Shilnikov
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06836
UR - https://arxiv.org/abs/2611.06836
AB - We study the dynamics of a delayed three-cell central pattern generator network using return-map analysis and a phase-reduced description derived from generalized FitzHugh-Nagumo oscillators. The phase model captures the emergence and stability of synchronous, pacemaker, and traveling-wave rhythms and provides a systematic, computationally efficient framework for characterizing the network dynamics beyond direct return-map calculations. We conduct extensive two-parameter analyses of both the full and phase-reduced models, revealing rich multi-rhythmic dynamics and transitions among coexisting rhythmic states. The close agreement between the two descriptions establishes phase reduction as an efficient and reliable framework for characterizing the dynamical organization of delayed neural oscillator networks.
ER -