Frequency bursts in adaptive delay-coupled oscillators
Abstract
We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.
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BibTeX
@misc{wang2026frequency,
title = {{Frequency bursts in adaptive delay-coupled oscillators}},
author = {Yu Wang and Jan Sieber and Jinde Cao and Jürgen Kurths and Serhiy Yanchuk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24671},
eprint = {2609.24671},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24671},
}
RIS
TY - UNPB
TI - Frequency bursts in adaptive delay-coupled oscillators
AU - Yu Wang
AU - Jan Sieber
AU - Jinde Cao
AU - Jürgen Kurths
AU - Serhiy Yanchuk
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.24671
UR - https://arxiv.org/abs/2609.24671
AB - We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.
ER -