# American Institute of Mathematical Sciences

October  2015, 8(5): 847-856. doi: 10.3934/dcdss.2015.8.847

## Reduced model from a reaction-diffusion system of collective motion of camphor boats

 1 Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810 2 Department of Mathematical Sciences Based on Modeling and Analysis, Meiji University, Nakano-ku, Tokyo, 164-8525 3 Research Institute for Electronic Science, Hokkaido University / JST CREST, Sapporo, 060-0812, Japan 4 Faculty of Engineering, Musashino University / JST CREST, Koto-ku, Tokyo, 135-8181, Japan

Received  December 2013 Revised  July 2014 Published  July 2015

Various motions of camphor boats in the water channel exhibit both a homogeneous and an inhomogeneous state, depending on the number of boats, when unidirectional motion along an annular water channel can be observed even with only one camphor boat. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Since the experimental results described above are thought of as a kind of bifurcation phenomena, we would like to investigate a linearized eigenvalue problem in order to prove the destabilization of a traveling wave solution. However, the eigenvalue problem is too difficult to analyze even if the number of camphor boats is 2. Hence we need to make a reduction on the model. In the present paper, we apply the center manifold theory and reduce the model to an ordinary differential system.
Citation: Shin-Ichiro Ei, Kota Ikeda, Masaharu Nagayama, Akiyasu Tomoeda. Reduced model from a reaction-diffusion system of collective motion of camphor boats. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 847-856. doi: 10.3934/dcdss.2015.8.847
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