  We investigate a cosmological scenario with three interacting components that
includes dark matter, dark energy, and radiation in the spatially flat
Friedmann-Robertson-Walker universe. We introduce a 3-dimensional internal
space, the interaction vector $\mathbf{Q}=(Q_{x}, Q_{m}, Q_{r})$ satisfying the
constraint plane $Q_{x}+ Q_{m}+ Q_{r}=0$, the barotropic index vector $
\boldmath ${\gamma}$=(\ga_x,\ga_m,\ga_r)$ and select a transversal interaction
vector $\mathbf{Q_t}$ in a sense that $\mathbf{Q_t}\cdot \boldmath
${\gamma}$=0$. We exactly solve the source equation for a linear
$\mathbf{Q_t}$, that depends on the total energy density and its derivatives up
to third order, and find all the component energy densities. We obtain a large
set of interactions for which the source equation admits a power law solution
and show its asymptotic stability by constructing the Lyapunov function. We
apply the $\chi^{2}$ method to the observational Hubble data for constraining
the cosmic parameters, and analyze the amount of dark energy in the radiation
era for the above linear $\mathbf{Q_t}$. It turns to be that our model fulfills
the severe bound of $\Omega_{x}(z\simeq 1100)<0.1$ and is consistent with the
future constraints achievable by Planck and CMBPol experiments.
