  The study of supernova neutrinos result an interesting non-linear phenomenon,
consisting of three phases: synchronized oscillation phase, bipolar flavor
conversion phase and the phase of spectral split. In the collective oscillation
of supernova neutrino the self energy is not a constant but varies
adiabatically, which is responsible to have such different phases. In this
article the transition point from synchronized oscillation to bipolar phase is
studied numerically as well as analytically. The numerical results yielding
different graphs depending on different values of possible small but
non-vanishing mixing angles show the onset of the bipolar phase from the
synchronized phase varies as the mixing angle. But the analytical study in
terms of a spinning top model results a unique onset condition, which is
independent of the choice of mixing angle. Such discrepancy between numerical
results and analytical results is explained properly.
