  We discuss the asymptotic dynamical evolution of spatially inhomogeneous
brane-world cosmological models close to the initial singularity. By
introducing suitable scale-invariant dependent variables and a suitable gauge,
we write the evolution equations of the spatially inhomogeneous $G_{2}$ brane
cosmological models with one spatial degree of freedom as a system of
autonomous first-order partial differential equations. We study the system
numerically, and we find that there always exists an initial singularity, which
is characterized by the fact that spatial derivatives are dynamically
negligible. More importantly, from the numerical analysis we conclude that
there is an initial isotropic singularity in all of these spatially
inhomogeneous brane cosmologies for a range of parameter values which include
the physically important cases of radiation and a scalar field source. The
numerical results are supported by a qualitative dynamical analysis and a
calculation of the past asymptotic decay rates. Although the analysis is local
in nature, the numerics indicates that the singularity is isotropic for all
relevant initial conditions. Therefore this analysis, and a preliminary
investigation of general inhomogeneous ($G_0$) models, indicates that it is
plausible that the initial singularity is isotropic in spatially inhomogeneous
brane-world cosmological models and consequently that brane cosmology naturally
gives rise to a set of initial data that provide the conditions for inflation
to subsequently take place.
