Cosmological dynamics of f(R) models in dynamical system analysis

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.