  We have shown that the phenomenological models with a cosmological constant
of the type $\Lambda=\beta(\frac{\ddot R}{R})$ and $\Lambda=3\alpha H^2$, where
$R$ is the scale factor of the universe and $H$ is the Hubble constant, are
equivalent to a quintessence model with a scalar ($\phi$) potential of the form
$V\propto \phi^{-n}, n$ = constant. The equation of state of the cosmic fluid
is described by these parameters ($\alpha, \beta, n$) only. The equation of
state of the cosmic fluid (dark energy) can be determined by any of these
parameters. The actual amount of dark energy will define the equation of state
of the cosmic fluid. All of the three forms can give rise to cosmic
acceleration depending the amount of dark energy in the universe.
