Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth
Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth
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DOI：
10.1007/s13160-017-0298-0
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发表时间：
2018-07
影响因子：
0.9
通讯作者：
H. Izuhara;Kousuke Kuto;T. Tsujikawa
中科院分区：
文献类型：
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作者：
H. Izuhara;Kousuke Kuto;T. Tsujikawa
从斑图形成的观点出发，研究了具有增长项的Keller-Segel系统。这些模型表现出各种固定的和时空的模式，这是由三种效应的组合：趋化性，扩散和增长。本文考虑了在生物种群的迁移率趋于无穷大的极限情形下，具有生态学中Allee效应的三次增长项的Keller-Segel系统及其影子系统.我们证明了一维空间中影子系统定态解的存在性和稳定性。我们的证明是基于分歧理论，奇异摄动方法和水平集分析。我们还利用数值计算软件包给出了系统稳态解的整体结构的一些数值结果。此外，我们还借助计算机讨论了具有立方增长项的Keller-Segel系统与具有Logistic增长项的Keller-Segel系统在动力学上的差别。
From the viewpoint of pattern formation, Keller–Segel systems with growth terms are studied. These models exhibit various stationary and spatio-temporal patterns which are caused by a combination of three effects: chemotaxis, diffusion and growth. In this paper, we consider Keller–Segel system with the cubic growth term known as the Allee effect in ecology and itsshadow systemin the limiting case that the mobility of biological population tends to infinity. We show the existence and stability of stationary solutions of the shadow system in one space dimension. Our proof is based on the bifurcation theory, a singular perturbation method and a level set analysis. We also show some numerical results on global structures of stationary solutions in the systems by using AUTO package. Moreover, we mention the difference in dynamics between Keller–Segel system with the cubic growth term and that with the logistic growth term with the aid of a computer.