Dynamical system analysis of Dirac-Born-Infeld scalar field cosmology in coincident $f(Q)$ gravity

In this article, we offer the dynamical system analysis of the DBI (Dirac-Born-Infeld) scalar field in a modified $f(Q)$ gravity context. We have taken a polynomial form of modified gravity and used two different kinds of scalar potential, i.e., polynomial and exponential, and found a closed autonomous dynamical system of equations. We have analyzed the fixed points of such a system and commented on the conditions under which deceleration to late-time acceleration happens in this model. We have noted the similarity of the two models and have also shown that our result is indeed consistent with the previous work done on Einstein's gravity. We have also investigated the phenomenological implications of our models by plotting the EoS ($\omega$), Energy density ($\Omega$), and deceleration parameter ($q$) w.r.t. to e-fold time and comparing with the present value. Finally, we conclude the paper by observing how the dynamical system analysis differs in modified $f(Q)$ gravity, and we also provide some of the future scope of our work.