Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis / Fedotov S.,Ivanov A. O.,Zubarev A. Y. // MATHEMATICAL MODELLING OF NATURAL PHENOMENA. - 2013. - V. 8, l. 2. - P. 28-43.

ISSN/EISSN:

0973-5348 / нет данных

Type:

Article

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.

Author keywords:

anomalous random walks; cell migration; aggregation DIFFUSION; AGGREGATION; DISPERSAL; DYNAMICS; BEHAVIOR; SYSTEMS

DOI:

10.1051/mmnp/20138203

Web of Science ID:

ISI:000318215200003

Соавторы в МНС:

Другие поля

Поле	Значение
Publisher	EDP SCIENCES S A
Address	17, AVE DU HOGGAR, PA COURTABOEUF, BP 112, F-91944 LES ULIS CEDEX A, FRANCE
Language	English
Keywords-Plus	DIFFUSION; AGGREGATION; DISPERSAL; DYNAMICS; BEHAVIOR; SYSTEMS
Research-Areas	Mathematical \& Computational Biology; Mathematics; Science \& Technology - Other Topics
Web-of-Science-Categories	Mathematical \& Computational Biology; Mathematics, Interdisciplinary Applications; Multidisciplinary Sciences
Author-Email	sergei.fedotov@manchester.ac.uk
ResearcherID-Numbers	Zubarev, Adrey/B-4752-2014 Ivanov, Alexey/E-4442-2011
ORCID-Numbers	Ivanov, Alexey/0000-0001-8239-4039
Funding-Acknowledgement	Federal Programme {[}N 14.A18.21.0867]; EPSRC {[}EP/J019526/1]
Funding-Text	The authors gratefully acknowledge the support of the Federal Programme N 14.A18.21.0867. SF acknowledges the warm hospitality of Department of Mathematical Physics, Ural Federal University. SF also acknowledges the support of the EPSRC Grant EP/J019526/1. The authors wish to thank S. Falconer for interesting discussions.
Number-of-Cited-References	37
Usage-Count-Since-2013	11
Journal-ISO	Math. Model. Nat. Phenom.
Doc-Delivery-Number	134MV