  Non-conformal attractor behavior is studied by solving non-conformal second
order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical
solutions of the relative decay rate of the enthalpy density, the inverse shear
and bulk Reynolds numbers, all exhibit universal patterns towards an ideal
fluid description at late stages, demonstrating the existence of non-conformal
hydrodynamic attractor. However, as a generic feature, the non-conformal
hydrodynamic attractor emerges only at late times, which differs drastically
from the behavior observed in conformal systems. The absence of the early-time
attractor in non-conformal fluids is a consequence of the early-time instable
mode, which arises from a positive-valued eigen-mode associated with the
free-streaming dynamics. To support practical simulations of hydrodynamics in
high-energy heavy-ion collisions, early-time attractor can be restored in a
mixture of the shear and the bulk viscous corrections, in which early-time
instable modes cancel approximately. Early-time non-conformal attractor is also
approachable, if the quadratic coupling between the bulk pressure and the
expansion rate is enhanced by at least a factor of two through the transport
coefficient $\delta_{\Pi\Pi}$.
