  The resonance frequencies and oscillation phases of three acoustically
coupled bubbles are examined to show that avoided crossings can appear in a
multibubble system. Via a simple coupled oscillator model, we show that if at
least three bubbles exist, it is possible for their resonance frequencies as
functions of the separation distances between the bubbles to experience an
avoided crossing. Furthermore, by focusing our attention on the oscillation
phases and based on analysis of the transition frequencies [M. Ida, Phys. Lett.
A 297, 210 (2002); M. Ida, J. Phys. Soc. Jpn. 71, 1214 (2002)] of the coupled
bubbles, we show that a distinct state exchange takes place between the bubbles
at a point in the avoided crossing region, where a resonance frequency of the
triple-bubble system crosses with a transition frequency not corresponding to
the resonance frequencies.
