  Considering the Universe as a dynamic system, the understanding of its
evolution is an interesting aspect of study in cosmology. Here, we investigate
the anisotropic locally rotationally symmetric (LRS) Bianchi type-I (LRS-BI)
spacetime under the $f(Q)$ gravity of symmetric teleparallel theory equivalent
to the GR (STEGR) as a dynamical system and try to understand the role of
anisotropy in the evolution of its various phases. For this work, we consider
two models, viz., $f(Q) = -\,(Q+ 2\Lambda)$ and $f(Q) = -\, \beta Q^{n}$ to
study the critical points and stability of the LRS-BI Universe. In both the
models, it is found that the various phases like radiation-dominated,
matter-dominated, and dark energy-dominated phases are heteroclinically
connected, and there is some role of anisotropy in the evolution of these
phases of the Universe. However, for both the models, there are some unphysical
solutions too depending upon the values of model parameters $\beta$ and $n$
along with the anisotropic parameter $\alpha$.
