期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 241, 期 19, 页码 1629-1639出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2012.06.009
关键词
Bifurcation; Chemotaxis; Pattern formation
资金
- Ministry of Education, Science, Sports and Culture in Japan [B 24740101, B 22740112, B 22740249]
- Grants-in-Aid for Scientific Research [22740112, 24740101] Funding Source: KAKEN
Minima 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. (C) 2012 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据