  We investigated self-sustained oscillation in a collapsible channel, in which
a part of one rigid wall is replaced by a thin elastic wall, and
synchronization phenomena in the two channels connected in parallel. We
performed a two-dimensional hydrodynamic simulation in a pair of collapsible
channels which merged into a single channel downstream. The stable
synchronization modes depended on the distance between the deformable region
and the merging point; only an in-phase mode was stable for the large distance,
in-phase and antiphase modes were bistable for the middle distance, and again
only an in-phase mode was stable for the small distance. An antiphase mode
became stable through the subcritical pitchfork bifurcation by decreasing the
distance. Further decreasing the distance, the antiphase mode became unstable
through the subcritical Neimark-Sacker bifurcation. We also clarified the
distance dependences of the amplitude and frequency for each stable
synchronization mode.
