  Two parallel stacks of coupled Josephson junctions are investigated to
clarify the physics of transitions between the rotating and oscillating states
and their effect on the IV-characteristics of the system. The detailed study of
phase dynamics and bias dependence of the superconducting and diffusion
currents allows one to explain all features of simulated IV-characteristics and
demonstrate the correspondence in their behavior. The coupling between JJ in
the stacks leads to the branching of IV-characteristics and a decrease in the
hysteretic region. The crucial role of the diffusion current in the formation
of the IV-characteristic of the parallel stacks of coupled Josephson junctions
is demonstrated. We discuss the effect of symmetry in a number of junctions in
the stacks and show a decrease of the branching in the symmetrical stacks. The
observed effects might be useful for development of superconducting electronic
devices based on intrinsic Josephson junctions.
