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Networks and Heterogeneous Media

2009, Volume 4, Issue 1: 1-18. doi: 10.3934/nhm.2009.4.1
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Self--motion of camphor discs. model and analysis

  • 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
  • Received: 01 July 2008 Revised: 01 October 2008

  • Primary: 80A30, 58J55, 35K55, 35K57; Secondary: 93A30.

  • 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.

    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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  • 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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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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