  In this work we try to understand the late time acceleration of the universe
by assuming some modification in the geometry of the space and using dynamical
system analysis. This technique allows to understand the behavior of the
universe without analytically solving the field equations. We study the
acceleration phase of the universe and stability properties of the critical
points which could be compared with observational results. We consider an
asymptotic behavior of two particular models $f(R) = R - \mu R_{c}
\frac{(R/R_c)^{2n}}{(R/R_c)^{2n} + 1}$ and $f(R) = R - \mu R_{c} \left[ 1 - (1
+ R^2/R_{c}^2)^{-n} \right]$ with $n,\mu, R_c >0$ for the study. As a first
case we fix the value of $\mu$ and analyzed for all $n$. Later as second case,
we fix the value of $n$ and calculation are done for all $\mu$. At the end all
the calculations for the generalized case have been shown and results have been
discussed in detail.
