Stationary solutions for some shadow system of the Keller-Segel model with logistic growth
Stationary solutions for some shadow system of the Keller-Segel model with logistic growth
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DOI：
10.3934/dcdss.2015.8.1023
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
T. Tsujikawa;Kousuke Kuto;Yasuhito Miyamoto;H. Izuhara
中科院分区：
文献类型：
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作者：
T. Tsujikawa;Kousuke Kuto;Yasuhito Miyamoto;H. Izuhara
从斑图形成的观点出发，研究了具有增长项的Keller-Segel系统。该模型表现出由趋化性、扩散性和生长性三种效应共同作用所引起的各种静态和动态模式。在趋化效应很强的特殊情况下，[1]、[22]中的一些数值实验显示了静态和混沌模式。在本文中，我们考虑的增长和阴影系统的扩散系数和趋化强度增长到无穷大的极限情况下的逻辑源。在一维情况下，我们得到了影子系统稳态解的全局结构。我们的证明是基于分歧，奇异摄动和水平集分析。此外，我们还利用数值模拟软件包给出了解的全局分支分支的一些数值结果。
From a viewpoint of the pattern formation, the Keller-Segel system with the growth term is studied. This model exhibited various static and dynamic patterns caused by the combination of three effects, chemotaxis, diffusion and growth. In a special case when chemotaxis effect is very strong, some numerical experiment in [1],[22] showed static and chaotic patterns. In this paper we consider the logistic source for the growth and a shadow system in the limiting case that a diffusion coefficient and chemotactic intensity grow to infinity. We obtain the global structure of stationary solutions of the shadow system in the one-dimensional case. Our proof is based on the bifurcation, singular perturbation and a level set analysis. Moreover, we show some numerical results on the global bifurcation branch of solutions by using AUTO package.