  Many models have been developed to study the role of branching actin networks
in motility. One important component of those models is the distribution of
filament orientations relative to the cell membrane. Two mean-field models
previously proposed are generalized and analyzed. In particular, we find that
both models uniquely select for a dominant orientation pattern. In the linear
case, the pattern is the eigenfunction associated with the principal
eigenvalue. In the nonlinear case, we show there exists a unique equilibrium
and that the equilibrium is locally stable. Approximate techniques are then
used to provide evidence for global stability.
