Mathematical models of cell self-organization
Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–Segel system and Mimura’s system are able to...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X11000083 |
| Summary: | Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–Segel system and Mimura’s system are able to explain two elementary processes underlying qualitative behaviors of populations and complex patterns: oriented drift by chemoattraction and colony growth with local nutrient depletion.
More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions. |
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| ISSN: | 1110-256X |