  We investigate the multiple bifurcations in periodic orbit families in the
potential field of a highly irregular-shaped celestial body. Topological cases
of periodic orbits and four kinds of basic bifurcations in periodic orbit
families are studied. Multiple bifurcations in periodic orbit families consist
of four kinds of basic bifurcations. We found both binary period-doubling
bifurcations and binary tangent bifurcations in periodic orbit families around
asteroid 433 Eros. The periodic orbit family with binary period-doubling
bifurcations is nearly circular, with almost zero inclination, and is reversed
relative to the body of the asteroid 433 Eros. This implies that there are two
stable regions separated by one unstable region for the motion around this
asteroid. In addition, we found triple bifurcations which consist of two real
saddle bifurcations and one period-doubling bifurcation. A periodic orbit
family generated from an equilibrium point of asteroid 433 Eros has five
bifurcations, which are one real saddle bifurcation, two tangent bifurcations,
and two period-doubling bifurcations.
