title: Oscillatory motion of a camphor grain in a one-dimensional finite region.
abstract: 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.
authors.affiliation: Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan.
authors.forename: Yuki
authors.initials: Y
authors.lastname: Koyano
authors.affiliation: Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan.
authors.forename: Tatsunari
authors.initials: T
authors.lastname: Sakurai
authors.affiliation: Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan.
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Kitahata