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arXiv · 1606.04196

Oscillatory Motion of a Camphor Grain in a One-Dimensional Finite Region

Yuki Koyano·Tatsunari Sakurai·Hiroyuki Kitahata
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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.

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Yuki Koyano, Tatsunari Sakurai, Hiroyuki Kitahata. 2016-06-14. Oscillatory Motion of a Camphor Grain in a One-Dimensional Finite Region. https://doi.org/10.1103/physreve.94.042215

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