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

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Title: Reduced model from a reaction-diffusion system of collective motion of camphor boats
Authors: Ei, Shin-Ichiro Browse this author →KAKEN DB
Ikeda, Kota Browse this author →KAKEN DB
Nagayama, Masaharu Browse this author →KAKEN DB
Tomoeda, Akiyasu Browse this author
Keywords: Center manifold theory
traveling wave solution
collective motion
Issue Date: Oct-2015
Publisher: American Institute of Mathematical Sciences (AIMS)
Journal Title: Discrete and continuous dynamical systems series S
Volume: 8
Issue: 5
Start Page: 847
End Page: 856
Publisher DOI: 10.3934/dcdss.2015.8.847
Abstract: 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.
Rights: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in "Discrete and Continuous Dynamical Systems - Series S (DCDS-S)" following peer review. The definitive publisher-authenticated version Pages: 847 - 856, Volume 8, Issue 5, October 2015 is available online at:
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 栄 伸一郎

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