  We investigate a generic two-field Cahn-Hilliard model with variational and
nonvariational coupling. It describes, for instance, passive and active ternary
mixtures, respectively. Already a linear stability analysis of the homogeneous
mixed state shows that activity not only allows for the usual large-scale
stationary (Cahn-Hilliard) instability of the well known passive case but also
for small-scale stationary (Turing) and large-scale oscillatory (Hopf)
instabilities. In consequence of the Turing instability, activity may
completely suppress the usual coarsening dynamics. In a fully nonlinear
analysis we first briefly discuss the passive case before focusing on the
active case. Bifurcation diagrams and selected direct time simulations are
presented that allow us to establish that nonvariational coupling (i) can
partially or completely suppress coarsening and (ii) may lead to the emergence
of drifting and oscillatory states. Throughout, we emphasize the relevance of
conservation laws and related symmetries for the encountered intricate
bifurcation behavior.
