Spatial pattern formation in a chemotaxis-diffusion-growth model
Spatial pattern formation in a chemotaxis-diffusion-growth model
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DOI：
10.1016/j.physd.2012.06.009
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发表时间：
2012-10-01
影响因子：
4
通讯作者：
Tsujikawa, Tohru
中科院分区：
文献类型：
--
作者：
Kuto, Kousuke;Osaki, Koichi;Tsujikawa, Tohru
Minima和另一位作者（1996）提出了一个具有趋化性的生物个体聚集区域模式动力学的数学模型。对于该模型，Tello和Winkler(2007)[22]获得了从正常数解分叉的非恒定平稳解的无穷多个局部分支，而Kurata等人（2008）在数值上显示了矩形中的几种时空模式。在他们工作的激励下，我们从全局和局部（分岔）的角度考虑了平稳解的一些定性行为。首先研究了趋化强度趋于无穷时平稳解的渐近行为。其次，构造了栖息域为矩形的特殊情况下的条形和六边形平稳解的局部分岔分支。在这种情况下，还得到了分支在分岔点附近的方向。最后，我们给出了平稳型和振荡型的几个数值结果。(C) 2012 Elsevier B.V.版权所有
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.