Interacting dark energy: generic cosmological evolution for two scalar fields

We study the cosmological evolution of two coupled scalar fields with an arbitrary interaction term V_T(\phi,\vp) in the presence of a barotropic fluid, which can be matter or radiation. The force between the barotropic fluid and the scalar fields is only gravitational. We show that the dynamics is completely determine by only three parameters L_i i=1,2,3. We determine all critical points and study their stability. We find six different attractor solutions depending on the values of L_i and we calculate the relevant cosmological parameters. We discuss the possibility of having one of the scalar fields as of dark energy while the other could be a scalar field redshifting as matter.