  Dynamical models of prototype gravastars are constructed and studied. The
models are the Visser-Wiltshire three-layer gravastars, in which an infinitely
thin spherical shell of a perfect fluid with the equation of state $p =
(1-\gamma)\sigma$ divides the whole spacetime into two regions, where the
internal region is de Sitter, and the external is Schwarzschild. When $\gamma <
1$ and $\Lambda \not= 0$, it is found that in some cases the models represent
stable gravastars, and in some cases they represent "bounded excursion" stable
gravastars, where the thin shell is oscillating between two finite radii, while
in some other cases they collapse until the formation of black holes. However,
when $\gamma \ge 1$, even with $\Lambda \not= 0$, only black holes are found.
In the phase space, the region for both stable gravastars and "bounded
excursion" gravastars is very small in comparison to that of black holes,
although it is not completely empty.
