Spatial pattern formation in a chemotaxis-diffusion-growth model

Kousuke Kuto, Koichi Osaki, Tatsunari Sakurai, Tohru Tsujikawa*

*この研究の対応する著者

研究成果: Article査読

61 被引用数 (Scopus)

抄録

Mimura and one of the authors (1996) proposed a mathematical model for the pattern dynamics of aggregating regions of biological individuals possessing the property of chemotaxis. For this model, Tello and Winkler (2007) [22] obtained infinitely many local branches of nonconstant stationary solutions bifurcating from a positive constant solution, while Kurata et al. (2008) numerically showed several spatio-temporal patterns in a rectangle. Motivated by their work, we consider some qualitative behaviors of stationary solutions from global and local (bifurcation) viewpoints in the present paper. First we study the asymptotic behavior of stationary solutions as the chemotactic intensity grows to infinity. Next we construct local bifurcation branches of stripe and hexagonal stationary solutions in the special case when the habitat domain is a rectangle. For this case, the directions of the branches near the bifurcation points are also obtained. Finally, we exhibit several numerical results for the stationary and oscillating patterns.

本文言語English
ページ(範囲)1629-1639
ページ数11
ジャーナルPhysica D: Nonlinear Phenomena
241
19
DOI
出版ステータスPublished - 2012 10 1
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 凝縮系物理学
  • 応用数学

フィンガープリント

「Spatial pattern formation in a chemotaxis-diffusion-growth model」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル