Stability of accelerating cosmology in two scalar-tensor theory: Little
  Rip versus de Sitter
  We develop the general reconstruction scheme in two scalar model. The
quintom-like theory which may describe (different) non-singular Little Rip or
de Sitter cosmology is reconstructed. (In)stability of such dark energy
cosmologies as well as the flow to fixed points is studied. The stability of
Little Rip universe which leads to dissolution of bound objects sometime in
future indicates that no classical transition to de Sitter space occurs.
