  We have investigated the evolution of the neutrino asymmetry in
active-sterile neutrino oscillations in the early universe. We find that there
are large regions of parameter space where the asymmetry is extremely sensitive
to variations in the initial asymmetry as well as the external parameters (the
mass difference and the mixing angle). In these regions the system undergoes
chaotic transitions; however, the system is never truly chaotic in the sense
that all information about initial conditions is lost. In some cases though,
enough information is lost that the final sign of the neutrino asymmetry is
stochastic. We discuss the implications of our findings for Big Bang
nucleosynthesis (BBN) and the cosmic microwave background (CMB).
