open access

https://hdl.handle.net/2115/63372

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

英語

collective motion

2015-10

American Institute of Mathematical Sciences (AIMS)

Discrete and continuous dynamical systems series S

8(5)

847-856

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.

学術雑誌論文

Accepted Manuscript

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.

1937-1632

1937-1179