Eur. Phys. J. B 52, 433-443 (2006)
https://doi.org/10.1140/epjb/e2006-00310-y

Jeans type instability for a chemotactic model of cellular aggregation

Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France

Corresponding author: ^a chavanis@irsamc.ups-tlse.fr

Received: 6 March 2006
Revised: 23 May 2006
Published online: 2 August 2006

Abstract

We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells, ...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of the perturbation as a function of the cell density and the wavelength of the perturbation. We discuss the differences between overdamped (Keller-Segel) and inertial models. Finally, we show the analogy between the instability criterion for biological populations and the Jeans instability criterion in astrophysics.