  A simple one-dimensional mechanical model is proposed for splitting
instability in swollen membranes. The splitting instability occurs by ring
constriction. The bifurcation can be both subcritical and supercritical,
depending on the slenderness of spheroidal membranes. The lower critical point
is estimated theoretically for the simplest circular system. Necking
instability occurs in a spheroidal membrane when the twist angle in the
boundary conditions is increased.
