  In this paper we consider a class of weighted-volume preserving curvature
flows acting on hypersurfaces that are trapped within two parallel hyperplanes
and satisfy an orthogonal boundary condition. In the author's thesis the
stability of cylinders under the flows was considered; it was found that they
are stable provided the radius satisfies a certain condition. Here we consider
flows where there is a critical radius such that the cylinders are only stable
on one side of the critical value, and the weight function is a linear
combination of the elementary symmetric functions, the reason for such a choice
is made clear in the appendix. We find that in such instances bifurcation from
the cylindrical stationary solutions occurs at the critical radius and we
determine a condition on the speed and weight functions such that the nearby
non-cylindrical stationary solutions are stable under the flow. We will also
highlight the specific cases of homogeneous speed functions and the
mixed-volume preserving mean curvature flows.
