  Appearance and origin of resonance phenomena have been studied in the annular
system of underdamped Josephson junctions. If no fluxon is trapped in the
system, dynamics is governed by the motion of fluxon-antifluxon pairs, while if
trapped fluxons are present, they can move solely but also simultaneously with
the pairs. Locking between the rotating excitations (fluxons and antifluxons)
and the Josephson frequency leads to the appearance of zero field steps in the
current-voltage characteristics, which can further exhibit branching due to
resonance between the rotating excitations and plasma oscillations in their
tale. The number of zero field steps and their branching are strongly
determined by the total number of excitations present in the system. High
resolution analysis further reveals not only some interesting properties of
zero field steps, but also shows that the current-voltage characteristics is
determined not only by the number, but also by the type of excitations, i.e.,
whether the dynamics is governed only by the motion of fluxon-antifluxon pairs
or the trapped fluxons, or they move simultaneously in the system.
