We propose a new quintessence scenario in the brane cosmology , assuming that a quintessence field Q is confined in our 3-dimensional brane world .
With a potential V ( Q ) = \mu ^ { \alpha + 4 } Q ^ { - \alpha } ~ { } ( \alpha \geq 2 ) , we find that the density parameter of the scalar field decreases as \Omega _ { Q } \sim a ^ { -4 ( \alpha - 2 ) / ( \alpha + 2 ) } in the epoch of quadratic energy density dominance , if \alpha \leq 6 .
This attractor solution is followed by the usual tracking quintessence scenario after a conventional Friedmann universe is recovered .
With an equipartition of initial energy density , we find a natural and successful quintessence model for \alpha \mbox { \raisebox { -4.3 pt } { $ \stackrel { \textstyle > } { \textstyle \sim } $ } } 4 .