  We study tilted perfect fluid cosmological models with a constant equation of
state parameter in spatially homogeneous models of Bianchi type VI_h using
dynamical systems methods and numerical experimentation, with an emphasis on
their future asymptotic evolution. We determine all of the equilibrium points
of the type VI_h state space (which correspond to exact self-similar solutions
of the Einstein equations, some of which are new), and their stability is
investigated. We find that there are vacuum plane-wave solutions that act as
future attractors. In the parameter space, a `loophole' is shown to exist in
which there are no stable equilibrium points. We then show that a
Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer
to as the Mussel attractor) corresponding to points both inside the loophole
and points just outside the loophole; in the former case the closed curves act
as late-time attractors while in the latter case these attracting curves will
co-exist with attracting equilibrium points. In the special Bianchi type III
case, centre manifold theory is required to determine the future attractors.
Comprehensive numerical experiments are carried out to complement and confirm
the analytical results presented. We note that the Bianchi type VI_h case is of
particular interest in that it contains many different subcases which exhibit
many of the different possible future asymptotic behaviours of Bianchi
cosmological models.
