  The motion of a self-propelled particle is affected by its surroundings, such
as boundaries or external fields. In this paper, we investigated the
bifurcation of the motion of a camphor grain, as a simple actual self-propelled
system, confined in a one-dimensional finite region. A camphor grain exhibits
oscillatory motion or remains at rest around the center position in a
one-dimensional finite water channel, depending on the length of the water
channel and the resistance coefficient. A mathematical model including the
boundary effect is analytically reduced to an ordinary differential equation.
Linear stability analysis reveals that the Hopf bifurcation occurs, reflecting
the symmetry of the system.
