Asymptotic states in brane cosmology with a nonlocal anisotropic stress

We investigate the dynamics of a Bianchi I brane Universe in the presence of a nonlocal anisotropic stress ${cal P}_{mu u}$ proportional to a dark energy ${cal U}$. Using this ansatz for the case ${cal U} > 0$ we prove that if a matter on a brane satisfies the equation of state $p=(gamma-1)rho$ with $gamma le 4/3$ then all such models isotropize. For $gamma > 4/3$ anisotropic future asymptotic states are found. We also describe the past asymptotic regimes for this model.