  In dense neutrino gases, the neutrino-neutrino coherent forward scattering
gives rise to a complex flavor oscillation phenomenon not fully incorporated in
simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe).
Moreover, it has been proposed to be chaotic, potentially limiting our ability
to predict neutrino flavor transformations in simulations. To address this
issue, we explore how small flavor perturbations evolve within a narrow
centimeter-scale region inside a NSM and a toy neutrino distribution. Our
findings reveal that paths in the flavor state space of solutions with similar
initial conditions diverge exponentially, exhibiting chaos. This inherent chaos
makes the microscopic scales of neutrino flavor transformations unpredictable.
However, the domain-averaged neutrino density matrix remains relatively stable,
with chaos minimally affecting it. This particular property suggests that
domain-averaged quantities remain reliable despite the exponential
amplification of errors.
