ABSTRACT : In this paper , we describe a way to construct a class of dark energy models that admit 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 non-vanishing minimum while this condition becomes that the potentials have non-vanishing 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 .