  We investigate the dynamical behavior of the Gross-Pitaevskii equation for a
Bose-Einstein condensate trapped in a spherical power law potential restricted
to the repulsive case, from the dynamical system formalism point of view. A
five-dimensional dynamical system is found (due the symmetry of the
Gross-Pitaevskii equation interacting with a potential), where the Thomas-Fermi
approximation constrains the parameter space of solutions. We show that for
values of the power law exponent equal or smaller than 2 the system seems to be
stable. However, when the corresponding exponent is bigger than 2, the
instability of the system grows when the power law exponent grows, indicating
that large values of the aforementioned parameter can be related to a loss in
the number of particles from the condensed state. This fact can be used also to
show that the stability conditions of the condensate are highly sensitive to
the exponent associated with the external potential.
