  Motivated by the observation of localized circular excitations (`oscillons')
in vertically vibrated granular layers (P.B. Umbanhowar, F. Melo and H.L.
Swinney, Nature 382 (1996) 793), we numerically investigate an extension of a
Swift-Hohenberg model that exhibits a subcritical transition to square
patterns. For sufficient subcriticality, stable oscillon structures are found.
The localization mechanism is quite general and is due to non-adiabatic
effects. Bound structures of oscillons of equal and opposite polarity are found
with bound states of like polarity being less robust. Much of the phenomena are
consistent with the experimental observations and suggest that oscillons are
not specific to patterns in granular media or to parametrically driven systems.
Experimental tests are suggested that would determine whether this minimal
framework is sufficient to describe the phenomena.
