  We study the dynamics of the chiral phase transition expected during the
expansion of the quark-gluon plasma produced in a high energy hadron or heavy
ion collision in the $O(4)$ linear sigma model to leading order in a large $N$
expansion for strong coupling constants. Starting from an approximate
equilibrium configuration at an initial proper time $\tau$ in the disordered
phase, we study the transition to the ordered broken symmetry phase as the
system expands and cools. We give results for the proper time evolution of the
effective pion mass, the order parameter $<\sigma>$ as well as for the pion two
point correlation function expressed in terms of a time dependent phase space
number density and pair correlation density. We investigate the possibility of
disoriented chiral condensate being formed during the expansion. In order to
create large domains of disoriented chiral condensates low-momentum
instabilities have to last for long enough periods of time. Our simulations
show that instabilities that are formed during the initial stages of the
expansion survive for proper times that are at most $3\,fm/c$.
