  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.
