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Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis

Published online by Cambridge University Press:  24 April 2013

S. Fedotov ,
A. O. Ivanov  and
A. Y. Zubarev
S. Fedotov*
Affiliation:
School of Mathematics, The University of Manchester, Manchester, M13 9PL, UK
A. O. Ivanov
Affiliation:
Department of Mathematical Physics, Ural Federal University, Ekaterinburg, 620083, Russia
A. Y. Zubarev
Affiliation:
Department of Mathematical Physics, Ural Federal University, Ekaterinburg, 620083, Russia
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

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.

Keywords

anomalous random walkscell migrationaggregation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 28 - 43
Copyright
© EDP Sciences, 2013

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