  We describe the collective behavior of a system of many inelastic spherical
particles inside a box which is being periodically vibrated. The box is
shallow, with large horizontal dimensions, while the height is less than two
particle diameters. The vibrations are not symmetric: the time the box is
moving up is, in general, different to the time it is moving down. The limit
cycles of isolated grains are largely affected by the asymmetry of the
vibration mode, increasing the size in phase space of the chaotic regions. When
many grains are placed in the box, the phase separation between dense,
solid-like regions, coexisting with fluid-like regions takes place at smaller
global densities for asymmetric vibration profiles. Besides, the order
parameter of the transition takes larger values when asymmetric forcing is
used.
