  Inflaton coupling to a vector field via the $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$
term is used in several contexts in the literature, such as to generate
primordial magnetic fields, to produce statistically anisotropic curvature
perturbation, to support anisotropic inflation and to circumvent the
$\eta$-problem. Here, I perform dynamical analysis of such a system allowing
for most general Bianchi I initial conditions. I also confirm the stability of
attractor equilibrium points in phase-space directions that had not been
investigated before.
