Measure-valued death state and local sensitivity analysis for Winfree models with uncertain high-order couplings

TL;DR

This paper investigates the measure-valued death state and local sensitivity of the Winfree synchronization model with uncertain high-order couplings, providing frameworks for oscillator death and analyzing regularity propagation.

Contribution

It introduces new analytical frameworks for oscillator death and regularity propagation in the Winfree model with uncertainties, extending understanding of synchronization dynamics.

Findings

Frameworks for oscillator death depending on parameters and initial data

Propagation of regularity in random space demonstrated

Numerical tests confirm analytical results

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.