Measure-valued death state and local sensitivity analysis for Winfree models with uncertain high-order couplings
Analysis of PDEs
2025-06-13 v2
Abstract
We study the measure-valued death state and local sensitivity analysis of the Winfree model and its mean-field counterpart with uncertain high-order couplings. The Winfree model is the first mathematical model for synchronization, and it can cast as the effective approximation of the pulse-coupled model for synchronization, and it exhibits diverse asymptotic patterns depending on system parameters and initial data. For the proposed models, we present several frameworks leading to oscillator death in terms of system parameters and initial data, and the propagation of regularity in random space. We also present several numerical tests and compare them with analytical results.
Keywords
Cite
@article{arxiv.2404.14072,
title = {Measure-valued death state and local sensitivity analysis for Winfree models with uncertain high-order couplings},
author = {Seung-Yeal Ha and Myeongju Kang and Jaeyoung Yoon and Mattia Zanella},
journal= {arXiv preprint arXiv:2404.14072},
year = {2025}
}