  A number of physical processes show some form of bifurcation or periodic
splintering of a single distribution into two new ones. Recently, it has been
noted that cavity searches for interactions between photons and exotic fields
may also result in bifurcation[1]. This paper builds on previous simulations of
bifurcation of an optical beam in the presence of periodic focusing [2]. Here,
however, the focus is on predicting a shifting of the beam's position, defined
by the center of the energy density, that can result. Mathematical models are
described and the formalism for simulating bifurcation under complex conditions
is delineated.
