  We consider the scenario emerging from the dynamics of a generalized
$d$-brane in a $(d+1, 1)$ spacetime. The equation of state describing this
system is given in terms of the energy density, $\rho$, and pressure, $p$, by
the relationship $p = - A/\rho^{\alpha}$, where $A$ is a positive constant and
$0 < \alpha \le 1$. We discuss the conditions under which homogeneity arises
and show that this equation of state describes the evolution of a universe
evolving from a phase dominated by non-relativistic matter to a phase dominated
by a cosmological constant via an intermediate period where the effective
equation of state is given by $p = \alpha \rho$.
