  Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the
action of a resonant external field, is studied. This field produces a
spatio-temporal modulation of the trapping potential with the frequency close
to the transition frequency between the ground state and a higher energy level.
The evolution equations of fractional populations display a kind of critical
phenomena at a critical line on the manifold of the system parameters. It is
demonstrated that there exists a direct analogy between dynamical instability
at this line and critical phenomena at a critical line of a related averaged
system.
