Scaling solutions on a brane

We investigate the dynamics of a flat isotropic brane universe with two-component matter source: perfect fluid with the equation of state p = ((gamma) - 1)(rho) and a scalar field with a power-law potential V ~ (radical sign)(alpha). The index (alpha) can be either positive or negative. We describe solutions for which the scalar field energy density scales as a power law of the scale factor (the so-called scaling solutions). In the nonstandard brane regime when the brane is driven by the energy density square term these solutions are rather different from their analogues in standard cosmology. Particular attention is paid to the inverse square potential. Its dynamical properties in the nonstandard brane regime are in some sense analogous to those of the exponential potential in standard cosmology. Stability analysis of the scaling solutions is provided. We also describe solutions existing in regions of the parameter space where the scaling solutions are unstable or do not exist.