  This paper examines neutrino flavor evolution outside a supernova
neutrinosphere using a one-dimensional model that retains the non-linear nature
of neutrino-neutrino interactions as well as some aspects of the full geometry.
In some limiting cases analytic results can be obtained that display different
behavior from their counterparts in (linear) solar neutrino flavor evolution.
For more general cases, numerical solutions require extended numerical
algorithms to achieve stable solutions, and these solutions exhibit standard
chaotic behavior.
