Qualitative Stability Analysis of Cosmological Parameters in $f(T,B)$ Gravity

We analyze the cosmological solutions of $f(T,B)$ gravity using dynamical system analysis where $T$ is the torsion scalar and $B$ be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we consider $ f(T,B)=f_{0}(B^{k}+T^{m})$, where $k$ and $m$ are constants. For second model, we consider $f(T,B)=f_{0}T B$. We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For both models, we get four critical points. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. In both model, we evaluated density parameters such as $\Omega_{r}$, $\Omega_{m}$, $\Omega_{\Lambda}$ and $\omega_{eff}$ and deceleration parameter $(q)$ and find their suitable range of the parameter $\lambda$ for stability. For first model, we get $\omega_{eff}=-0.833,-0.166$ and for second model, we get $\omega_{eff}=-\frac{1}{3}$. This shows that both the models are in quintessence phase. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.