does. And we find that for some fixed points, the function $f(\lambda)$ affects either their values, e.g., for points $P_{4-10}$, or their stability properties, e.g., for points $P_{3,9}$. In other words, the dynamical properties of these points depend on the specific form of the potential. But some other fixed points, e.g., points $P_{1,2}$,are independent of the potential. The properties of these fixed points are satisfied by all scalar fields. We also find that there are two later time attractors, but the Universe is scalar-field dominated since $\rho_\gamma=0$ at these later time attractors.

The method developed by [@Fang-CQG; @Zhou-plb] can describe the dynamical behavior of the scalar field with potential of a more general form than, for example, an exponential potential [@Copeland-exponential; @Hao-PRD1; @Hao-PRD2; @Samart-Phantom; @Li-O(N); @Ferreira-scaling; @Hoogen-scaling; @Billyard-interaction; @Fu-phantom]. But it is not all-encompassing. If one wants to discuss the dynamical properties of a scalar field with an arbitrary potential, one needs to consider the higher-order derivatives of the potential $V(\phi)$. Hence the dynamical system will extend from four dimensions to infinite-dimensions. This infinite-dimensional dynamical system is still autonomic, but it is impossible to get all of its dynamical behavior unless one considers $\Gamma_c=1$ which just gives an exponential potential. 