  This paper presents an investigation of cosmological dynamics of tachyon
fluid coupled to varyingmass dark matter particles in the background of
spatially flat FLRW universe. The mechanism of varying mass particles scenario
assumes the mass of the dark matter depends on time t through the scalar field
${\phi}$ in the sense that the decaying of dark matter reproduces the scalar
field. First, we analyze the model from dynamical systems perspective by
converting the cosmological evolution equations into an autonomous system of
ordinary differential equations with a suitable transformation of variables. We
choose the mass of dark matter as exponential function of scalar field and the
exponential potential of the tachyon field is undertaken in such a way that the
autonomous system is reduced in three dimensional form. The critical points
obtained from the system are non-hyperbolic in nature. The center manifold
theory is employed to discuss the nature of the critical points. Numerical
investigation also carried out for some critical points. From this analysis, we
obtain dust dominated decelerated transient phase of the universe followed by
dark energy dominated scaling attractor alleviating the coincidence problem.
Next, we perform the statefinder diagnostic approach to compare our model to
${\Lambda}$CDM and finally we study the evolution of the Hubble parameter and
the distance modulus and compare this with observational data.
