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

• Ei, Shin-Ichiro

• Ikeda, Kota

• Nagayama, Masaharu

• Tomoeda, Akiyasu

抄録

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.

収録刊行物

• Discrete and continuous dynamical systems series S

  Discrete and continuous dynamical systems series S 8 (5), 847-856, 2015-10

  American Institute of Mathematical Sciences (AIMS)

キーワード

• Center manifold theory
• bifurcation
• traveling wave solution
• collective motion

詳細情報

• CRID: 1050282813995931648
• NII論文ID: 120005853055
• ISSN: 19371179
• ISSN: 19371632
• HANDLE: 2115/63372
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles