  We describe the classical two dimensinal nonlinear dynamics of cold atoms in
far-off-resonant donut beams. We show that there chaotic dynamics exists for
charge greater than unity, when the intensity of the beam is periodically
modulated. The two dimensional distributions of atoms in $(x,y)$ plane for
charge two are simulated. We show that the atoms will acumulate on several ring
regions when the system enters to regime of global chaos.
