title: Bifurcation phenomena of two self-propelled camphor disks on an annular field depending on system length.
abstract: Mode selection and bifurcation of a synchronized motion involving two symmetric self-propelled objects in a periodic one-dimensional domain were investigated numerically and experimentally by using camphor disks placed on an annular water channel. Newton's equation of motion for each camphor disk, whose driving force was the difference in surface tension, and a reaction-diffusion equation for camphor molecules on water were used in the numerical calculations. Among various dynamical behaviors found numerically, four kinds of synchronized motions (reversal oscillation, stop-and-move rotation, equally spaced rotation, and clustered rotation) were also observed in experiments by changing the diameter of the water channel. The mode bifurcation of these motions, including their coexistence, were clarified numerically and analytically in terms of the number density of the disk. These results suggest that the present mathematical model and the analysis of the equations can be worthwhile in understanding the characteristic features of motion, e.g., synchronization, collective motion, and their mode bifurcation.
authors.affiliation: Department of Mathematics, Graduate School of Science, Hokkaido University, Hokkaido 060-0810, Japan.
authors.forename: Kei
authors.initials: K
authors.lastname: Nishi
authors.affiliation: Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, Japan.
authors.forename: Ken
authors.initials: K
authors.lastname: Wakai
authors.affiliation: Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.
authors.forename: Tomoaki
authors.initials: T
authors.lastname: Ueda
authors.affiliation: Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.
authors.forename: Miyu
authors.initials: M
authors.lastname: Yoshii
authors.affiliation: Graduate School of Life Science, Hokkaido University, Hokkaido 060-0810, Japan.
authors.forename: Yumihiko S
authors.initials: YS
authors.lastname: Ikura
authors.affiliation: Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.
authors.forename: Hiraku
authors.initials: H
authors.lastname: Nishimori
authors.affiliation: Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan.
authors.forename: Satoshi
authors.initials: S
authors.lastname: Nakata
authors.affiliation: Research Institute for Electronic Science, Hokkaido University, Hokkaido 060-0811, Japan.|CREST, JST, Saitama 332-0012, Japan.
authors.forename: Masaharu
authors.initials: M
authors.lastname: Nagayama