  We investigate numerically conditions for order and chaos in the dynamics of
an interacting Bose- Einstein condensate (BEC) confined by an external trap cut
off by a hard-wall box potential. The BEC is stirred by a laser to induce
excitations manifesting as irregular spatial and energy oscillations of the
trapped cloud. Adding laser stirring to the external trap results in an
effective time-varying trapping frequency in connection with the dynamically
changing combined external+laser potential trap. The resulting dynamics are
analyzed by plotting their trajectories in coordinate phase space and in energy
space. The Lyapunov exponents are computed to confirm the existence of chaos in
the latter space. Quantum effects and trap anharmonicity are demonstrated to
generate chaos in energy space, thus confirming its presence and implicating
either quantum effects or trap anharmonicity as its generator. The presence of
chaos in energy space does not necessarily translate into chaos in coordinate
space. In general, a dynamic trapping frequency is found to promote chaos in a
trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved
by increasing the characteristic scale of the external trap with respect to the
condensate size.
