Hyperbolic models for chemosensitive movement
Hyperbolic models for chemosensitive movement
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DOI：
10.1142/s0218202502002008
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发表时间：
2002-07-01
影响因子：
3.5
通讯作者：
Hillen, T
中科院分区：
文献类型：
--
作者：
Hillen, T
化学敏感运动描述了个体对化学信号的主动取向。在细胞黏菌或鞭毛细菌的情况下，化学敏感运动导致聚集和图案形成。描述化学敏感运动的经典数学模型是基于扩散的patak - keller - segel模型。它的缺点是传播速度无限。相关的模型参数（运动性和化学敏感性）与人口统计有关。双曲模型尊重有限的传播速度和相关的模型参数（转弯速度，新选择速度的分布）是基于手头物种的个体运动模式。本文讨论了化学敏感运动的双曲模型（一维）和输运模型（二维），并与经典模型进行了比较。对于双曲和输运模型，回顾了以下主题：抛物线极限（在某些情况下导致patak - keller - segel模型），局部和全局存在性，渐近行为和矩闭包。矩闭方法导致基于卡塔尼奥热传导定律（电报方程）的模型。
Chemosensitive movement describes the active orientation of individuals on chemical signals. In cases of cellular slime molds or flagellated bacteria, chemosensitive movement leads to aggregation and pattern formation. The classical mathematical model to describe chemosensitive movement is the diffusion based Patlak-Keller-Segel model. It suffers from the drawback of infinite propagation speeds. The relevant model parameters (motility and chemosensitivity) axe related to population statistics. Hyperbolic models respect finite propagation speeds and the relevant model parameters (turning rate, distribution of new chosen velocities) are based on the individual movement patterns of the species at hand. In this paper hyperbolic models (in 1-D) and a transport model (in n-D) for chemosensitive movement are discussed and compared to the classical model. For the hyperbolic and transport models the following topics are reviewed: parabolic limit (which in some cases leads to the Patlak-Keller-Segel model), local and global existence, asymptotic behavior and moment closure. The moment closure approach leads to models based on Cattaneo's law of heat conduction (telegraph equation).