Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis
Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis
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非均匀随机游走、细胞的次扩散迁移和异常趋化性
DOI：
10.1051/mmnp/20138203
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发表时间：
2013
影响因子：
2.2
通讯作者：
Fedotov S
中科院分区：
文献类型：
--
作者：
Fedotov S
本文关注细胞异常次扩散传输的空间非均匀和时间非局部随机游走模型。从涉及结构化概率密度函数的马尔可夫模型开始，我们推导了细胞位置概率的非局部时间主方程和分数方程。我们推导出细胞密度的分数式福克-普朗克方程，并将该方程应用于异常趋化性问题。我们证明了分数次扩散方程相对于反常指数的部分变化的结构不稳定性。我们找到了在半无限域中发生细胞异常聚集的标准。
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We derive the fractional Fokker-Planck equation for the density of cells and apply this equation to the anomalous chemotaxis problem. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.