  Empirical evidence suggests a tantalising but unproven link between various
indicators of solar activity and the barycentric motion of the Sun. The latter
is exemplified by transitions between regular and more disordered motion
modulated by the motions of the giant planets, and rare periods of retrograde
motion with negative orbital angular momentum. An examination of the
barycentric motion of exoplanet host stars, and their stellar activity cycles,
has the potential of proving or disproving the Sun's motion as an underlying
factor in the complex patterns of short- and long-term solar variability
indices, by establishing whether such correlations exist in other planetary
systems. A variety of complex patterns of barycentric motions of exoplanet host
stars is demonstrated, depending on the number, masses and orbits of the
planets. Each of the behavioural types proposed to correlate with solar
activity are also evident in exoplanet host stars: repetitive patterns
influenced by massive multiple planets, epochs of rapid change in orbital
angular momentum, and intervals of negative orbital angular momentum. The study
provides the basis for independent investigations of the widely-studied but
unproven suggestion that the Sun's motion is somehow linked to various
indicators of solar activity. We show that, because of the nature of their
barycentric motions, the host stars HD168443 and HD74156 offer particularly
powerful tests of this hypothesis.
