Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Ei, Shin-Ichiro, et al. "Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats." Mathematica Bohemica 139.2 (2014): 363-371. <http://eudml.org/doc/261898>.

@article{Ei2014,
abstract = {Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices 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 disks or 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.},
author = {Ei, Shin-Ichiro, Ikeda, Kota, Nagayama, Masaharu, Tomoeda, Akiyasu},
journal = {Mathematica Bohemica},
keywords = {center manifold theory; bifurcation; traveling wave solution; collective motion; center manifold theory; bifurcation; traveling wave solution; collective motion},
language = {eng},
number = {2},
pages = {363-371},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats},
url = {http://eudml.org/doc/261898},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Ei, Shin-Ichiro
AU - Ikeda, Kota
AU - Nagayama, Masaharu
AU - Tomoeda, Akiyasu
TI - Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 363
EP - 371
AB - Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices 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 disks or 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.
LA - eng
KW - center manifold theory; bifurcation; traveling wave solution; collective motion; center manifold theory; bifurcation; traveling wave solution; collective motion
UR - http://eudml.org/doc/261898
ER -