  I-V characteristics of the high T$_c$ superconductor
Bi$_2$Sr$_2$Ca$_1$C$_2$O$_8$ shows a strong hysteresis, producing many
branches. The origin of hysteresis jumps is studied by use of the model of
multi-layered Josephson junctions proposed by one of the authors (T. K.). The
charging effect at superconducting layers produces a coupling between the next
nearest neighbor phase-differences, which determines the structure of
hysteresis branches. It will be shown that a solution of phase motions is
understood as a combination of rotating and oscillating phase-differences, and
that, at points of hysteresis jumps, there occurs a change in the number of
rotating phase-differences. Effects of dissipation are analyzed. The
dissipation in insulating layers works to damp the phase motion itself, while
the dissipation in superconducting layers works to damp relative motions of
phase-differences. Their effects to hysteresis jumps are discussed.
