  In this paper, we investigate a non-canonical scalar field model in the
background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi
type I universe where gravity is coupled minimally to scalar field which is
taken as dark energy and pressureless dust as dark matter are the main matter
content of the universe. We perform dynamical system analysis to characterize
the cosmological evolution of the model with and without interaction in the
dark sector separately. First, we convert the evolution equation into an
autonomous system of ordinary differential equations by using a suitable choice
of dimensionless variables, which are normalized over the Hubble scale. We
choose scalar field coupling and potential in such a way that the autonomous
system converted to a 2D system. Linear stability theory is employed to the
extracted critical points to find the nature. From the analysis, we find some
interesting cosmological scenarios, such as late-time scalar-field dominated
solutions, which evolve in the quintessence era, cannot solve the coincidence
problem. Accelerated scaling attractors are also obtained that correspond to
the late phase evolution in agreement with present observational data, and
these solutions also provide possible mechanisms to alleviate the coincidence
problem. A complete cosmic evolution is obtained from early inflation to a
late-time dark energy-dominated phase, connecting through a matter-dominated
transient phase of the universe. Furthermore, we find that for different values
of the interaction parameter $\alpha$, the evolutionary trajectories of the
Hubble parameter, and the distance modulus forecasted by the model are in quite
well agreement with observational datasets.

General Relativity and Quantum Cosmology