  By considering the potential parameter $\Gamma$ as a function of another
potential parameter $\lambda$[47], We successfully extend the analysis of
two-dimensional autonomous dynamical system of quintessence scalar field model
to the analysis of three-dimension, which makes us be able to research the
critical points of a large number of potentials beyond the exponential
potential exactly. We find that there are ten critical points in all, three
points $P_{3, 5, 6}$} are general points which are possessed by all
quintessence models regardless of the form of potentials and the rest points
are closely connected to the concrete potentials. It is quite surprising that,
apart from the exponential potential, there are a large number of potentials
which can give the scaling solution when the function
$f(\lambda)(=\Gamma(\lambda)-1)$ equals zero for one or some values of
$\lambda_{*}$ and if the parameter $\lambda_{*}$ also satisfies the condition
Eq.(16) or Eq.(17) at the same time. We give the differential equations to
derive these potentials $V(\phi)$ from $f(\lambda)$. We also find that, if some
conditions are satisfied, the de-Sitter-like dominant point $P_4$ and the
scaling solution point $P_9$(or $P_{10}$) can be stable simultaneously but
$P_9$ and $P_{10}$ can not be stable simultaneity. Although we survey scaling
solutions beyond the exponential potential for ordinary quintessence models in
standard general relativity, this method can be applied to other extensively
scaling solution models studied in literature[46] including coupled
quintessence, (coupled-)phantom scalar field, k-essence and even beyond the
general relativity case $H^2 \propto\rho_T^n$. we also discuss the disadvantage
of our approach.
