Constructing dark energy models with a late time de Sitter attractor

In this paper, we describe a way to construct a class of dark energy models that admits late time de Sitter attractor solution. In the canonical scalar and Born-Infeld scalar dark energy models, we show mathematically that a simple sufficient condition for the existence of a late time de Sitter-like attractor solution is that the potentials of the scalar field have a nonvanishing minimum while this condition becomes that the potentials have a nonvanishing maximum for the phantom models. These attractor solutions correspond to an equation of state w=-1 and a cosmic density parameter Omega(phi)=1, which are important features for a dark energy model that can meet the current observations.