Breakdown of Adiabatic Scaling and Noise-induced Functional Synchronization in Deeply Quiescent Excitable Systems
Abstract
Coherence resonance (CR) characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we investigate the stochastic dynamics of a 3D Sherman-Rinzel-Keizer (SRK) model driven by multiplicative Feller noise. We show that traditional extremal evaluations of CR encounter a "bathtub effect", a broad resonance valley that can lead to statistical inaccuracies. To address this, we propose a logarithmic centroid extraction method, which filters out stochastic jitter and recovers the underlying adiabatic Kramers scaling with high linearity. Furthermore, we identify the physical boundary where this adiabatic approximation breaks down under the strong-noise limit. Extending our analysis to gap-junction coupled systems, we observe a noise-induced transition from sub-threshold physiological shivering (characterized by statistical correlation but negligible functional output) to macroscopic functional synchronization. Our results provide a mathematical framework for extracting optimal noise intensities in broad energy valleys and offer insights into how quiescent biological systems utilize stochastic fluctuations for functional recovery.
Versions
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BibTeX
@misc{wu2026breakdown,
title = {{Breakdown of Adiabatic Scaling and Noise-induced Functional Synchronization in Deeply Quiescent Excitable Systems}},
author = {Yefan Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.06692},
eprint = {2605.06692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06692},
}
RIS
TY - UNPB
TI - Breakdown of Adiabatic Scaling and Noise-induced Functional Synchronization in Deeply Quiescent Excitable Systems
AU - Yefan Wu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2605.06692
UR - https://arxiv.org/abs/2605.06692
AB - Coherence resonance (CR) characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we investigate the stochastic dynamics of a 3D Sherman-Rinzel-Keizer (SRK) model driven by multiplicative Feller noise. We show that traditional extremal evaluations of CR encounter a "bathtub effect", a broad resonance valley that can lead to statistical inaccuracies. To address this, we propose a logarithmic centroid extraction method, which filters out stochastic jitter and recovers the underlying adiabatic Kramers scaling with high linearity. Furthermore, we identify the physical boundary where this adiabatic approximation breaks down under the strong-noise limit. Extending our analysis to gap-junction coupled systems, we observe a noise-induced transition from sub-threshold physiological shivering (characterized by statistical correlation but negligible functional output) to macroscopic functional synchronization. Our results provide a mathematical framework for extracting optimal noise intensities in broad energy valleys and offer insights into how quiescent biological systems utilize stochastic fluctuations for functional recovery.
ER -