A stochastic Keller-Segel model of chemotaxis
A stochastic Keller-Segel model of chemotaxis
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DOI：
10.1016/j.cnsns.2008.09.002
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发表时间：
2010-01-01
影响因子：
3.9
通讯作者：
Chavanis, Pierre-Henri
中科院分区：
文献类型：
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作者：
Chavanis, Pierre-Henri
我们介绍了随机模型的趋化性推广确定性凯勒-西格尔模型。这些模型包括波动，这是很重要的系统与小粒子数或接近临界点。根据Dean的方法，我们推导出细胞密度分布所满足的精确动力学方程。在平均场的极限，细胞之间的统计相关性被忽略，我们恢复的凯勒-西格尔模型的光滑密度场。我们还考虑流体动力学和动力学模型的趋化性，考虑到惯性的颗粒，并导致延迟的细胞的速度与趋化梯度的调整。我们把它与卡塔内奥趋化模型和电报方程联系起来。(C)2008 Elsevier B. V.保留所有权利。
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cells are neglected, we recover the Keller-Segel model governing the smooth density field. We also consider hydrodynamic and kinetic models of chemotaxis that take into account the inertia of the particles and lead to a delay in the adjustment of the velocity of cells with the chemotactic gradient. We make the connection with the Cattaneo model of chemotaxis and the telegraph equation. (C) 2008 Elsevier B.V. All rights reserved.