Generalized Keller-Segel models of chemotaxis. Analogy with nonlinear mean field Fokker-Planck equations

Details Generalized Keller-Segel models of chemotaxis. Analogy with nonlinear mean field Fokker-Planck equations Generalized Keller-Segel models of chemotaxis. Analogy with nonlinear mean field Fokker-Planck equations

2008-09-29

arxiv.org/abs/0809.4982v1

Chandre, Leoncini, Zaslavsky Eds., Chaos, Complexity and Transport: Theory and Applications, World Scientific (2008) p. 265

Physics

Biological Physics

Proceedings of the conference "Chaos, Complexity and Transport" (Marseille, 5-9 June 2007)

Scientific paper

We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.

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