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

Abstract

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.

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

References in corpus (2)

• Jeans type analysis of chemotactic collapse
• Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars