We analyze the dynamics of a Dirac-Born-Infeld ( DBI ) field in a cosmological set-up which includes a perfect fluid .
Introducing convenient dynamical variables , we show the evolution equations form an autonomous system when the potential and the brane tension of the DBI field are arbitrary power-law or exponential functions of the DBI field .
In particular we find scaling solutions can exist when powers of the field in the potential and warp-factor satisfy specific relations .
A new class of fixed-point solutions are obtained corresponding to points which initially appear singular in the evolution equations , but on closer inspection are actually well defined .
In all cases , we perform a phase-space analysis and obtain the late-time attractor structure of the system .
Of particular note when considering cosmological perturbations in DBI inflation is a fixed-point solution where the Lorentz factor is a finite large constant and the equation of state parameter of the DBI field is w = -1 .
Since in this case the speed of sound c _ { s } becomes constant , the solution can be thought to serve as a good background to perturb about .