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Reduced model from a reaction-diffusion system of collective motion of camphor boats
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 | bifurcation | 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: http://dx.doi.org/10.3934/dcdss.2015.8.847. |
Type: | article (author version) |
URI: | http://hdl.handle.net/2115/63372 |
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)
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Submitter: 栄 伸一郎
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