  In background dynamics of a spatially flat FLRW model of the universe, we
investigate an interacting scenario of quintessence scalar field as dark energy
which interacts with pressure-less dust as dark matter, mass of which varies
with time through scalar field in context of Lyra's geometry. Mass of dark
matter particles and the potential of the quintessence field are considered to
be functions depending exponentially on scalar field. Cosmological evolution
equations in this context are converted into an autonomous system of ordinary
differential equations by suitable transformation of the cosmological variables
into dimensionless dynamical variables and the nature of critical points are
found by applying linear stability theory. We have obtained cosmologically
interested critical points which describe the attractor solutions at late
times. Some of which representing the accelerated scalar field-dark matter
scaling solutions in attractor regime with similar order of energy densities
can provide the possible solution of the coincidence problem.
