Self--motion of camphor discs. model and analysis

2009, Volume 4, Issue 1: 1-18. doi: 10.3934/nhm.2009.4.1

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1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.
Faculty of Mathematics, Kyushu University, Fukuoka, 812-8581
3.
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571

In the present paper, a model describing the self-motion of a camphor disc on water is proposed. The stability of a standing camphor disc is investigated by analyzing the model equation, and a pitchfork type bifurcation diagram of a traveling spot is shown. Multiple camphor discs are also treated by the model equations, and the repulsive interaction of spots is discussed.
- camphor discs,
- repulsive interaction,
- center manifold theory,
- traveling spot
Citation: Xinfu Chen, Shin-Ichiro Ei, Masayasu Mimura. Self--motion of camphor discs. model and analysis[J]. Networks and Heterogeneous Media, 2009, 4(1): 1-18. doi: 10.3934/nhm.2009.4.1

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Abstract

In the present paper, a model describing the self-motion of a camphor disc on water is proposed. The stability of a standing camphor disc is investigated by analyzing the model equation, and a pitchfork type bifurcation diagram of a traveling spot is shown. Multiple camphor discs are also treated by the model equations, and the repulsive interaction of spots is discussed.
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