%0 Journal Article %T General Criteria for Determining Rotation or Oscillation in a Two-dimensional Axisymmetric System %A Yuki Koyano %A Natsuhiko Yoshinaga %A Hiroyuki Kitahata %J Physics %D 2014 %I arXiv %R 10.1063/1.4923421 %X A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion. %U http://arxiv.org/abs/1411.2409v5