趋化性
稳态(化学)
图案形成
同种类的
非线性系统
统计物理学
符号(数学)
过渡(遗传学)
类型(生物学)
过渡点
生物系统
物理
数学
机械
热力学
控制理论(社会学)
化学
数学分析
计算机科学
物理化学
生物
生态学
量子力学
生物化学
控制(管理)
受体
遗传学
人工智能
基因
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2014-01-01
卷期号:19 (9): 2809-2835
被引量:8
标识
DOI:10.3934/dcdsb.2014.19.2809
摘要
The main objective of this article is to study the dynamic transition and pattern formation for chemotactic systems modeled by the Keller-Segel equations. We study chemotactic systems with either rich or moderated stimulant supplies. For the rich stimulant chemotactic system, we show that the chemotactic system always undergoes a Type-I or Type-II dynamic transition from the homogeneous state to steady state solutions. The type of transition is dictated by the sign of a non dimensional parameter $b$, which is derived by incorporating the nonlinear interactions of both stable and unstable modes. For the general Keller-Segel model where the stimulant is moderately supplied, the system can undergo a dynamic transition to either steady state patterns or spatiotemporal oscillations. From the pattern formation point of view, the formation and the mechanism of both the lamella and rectangular patterns are derived.
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