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

TL;DR

This paper explores a generalized Keller-Segel model for chemotaxis, highlighting its analogy with nonlinear mean field Fokker-Planck equations and introducing a new model that includes anomalous diffusion and volume filling effects.

Contribution

It introduces a novel chemotaxis model incorporating anomalous diffusion and exclusion principles, and draws analogies with nonlinear thermodynamics and self-gravitating systems.

Findings

Established analogy with nonlinear mean field Fokker-Planck equations

Proposed a new chemotaxis model with anomalous diffusion and volume filling

Linked biological chemotaxis to self-gravitating Brownian particles

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.