  Utilizing the autonomous system of ordinary differential equations derived in
arXiv:1809.01458 to define the evolution, we further investigate a class of
cosmological models within an Einstein-aether gravitational framework by
introducing a non-trivial coupling between the shear of the aether field to the
scalar field on the future asymptotic solution. We subsequently conduct
qualitative and numerical stability analysis on the new set of equilibrium
points and paramountly determine that the expansionary power-law inflationary
attractor becomes anisotropic rather than isotropic in the presence of such a
coupling. It is further shown that the stability of this solution is dependent
on the value of the shear coupling parameter $a3$. We also discover a family of
asymptotically stable periodic orbits which exist for a particular range of
parameter values within the Bianchi I invariant set and vanish in the absence
of coupling between the aether field and the scalar field.
