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Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to theaction of a resonant external field, is studied. This field produces aspatio-temporal modulation of the trapping potential with the frequency closeto the transition frequency between the ground state and a higher energy level.The evolution equations of fractional populations display a kind of criticalphenomena at a critical line on the manifold of the system parameters. It isdemonstrated that there exists a direct analogy between dynamical instabilityat this line and critical phenomena at a critical line of a related averagedsystem.Comment: Latex file, 7 pages, no figure

Dynamic critical phenomena in trapped Bose gases