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.
Similar content being viewed by others
References
J.D. Murray, Mathematical Biology (Springer, Berlin, 1991)
E. Keller, L.A. Segel, J. theor. Biol. 26, 399 (1970)
A. Gamba et al., Phys. Rev. Lett. 90, 118101 (2003)
F. Filbet, P. Laurençot, B. Perthame, J. Math. Biol. 50, 189 (2005)
J. Peebles, Large-Scale Structure of the Universe (Princeton University Press, 1980)
M. Vergassola, B. Dubrulle, U. Frisch, A. Noullez, Astron. Astrophys. 289, 325 (1994)
P.H. Chavanis, J. Sommeria, R. Robert, Astrophys. J. 471, 385 (1996)
P.H. Chavanis, Phys. Rev. E 68, 036108 (2003)
P.H. Chavanis, M. Ribot, C. Rosier, C. Sire, Banach Center Publ. 66, 103 (2004)
P.H. Chavanis, C. Sire, Phys. Rev. E 73, 066103 (2006); Phys. Rev. E 73, 066104 (2006)
P.H. Chavanis, C. Rosier, C. Sire, Phys. Rev. E 66, 036105 (2002)
J.H. Jeans, Astronomy and Cosmogony (Cambridge University Press, 1929)
W. Jäger, S. Luckhaus, Trans. Am. Math. Soc. 329, 819 (1992)
J.P. Cox, Theory of Stellar Pulsation (Princeton Series in Astrophysics, 1980)
J. Binney, S. Tremaine, Galactic Dynamics (Princeton Series in Astrophysics, 1987)
P. Carmeliet, Nature Medicine 6, 389 (2000)
J. Lega, T. Passot, Phys. Rev. E 67, 031906 (2003)
N.H. Mendelson et al., J. Bacteriol. 181, 600 (1999)
D. Horstmann, Jahresberichte der DMV 106, 51 (2004)
C. Sire, P.H. Chavanis, Phys. Rev. E 66, 046133 (2002)
C. Sire, P.H. Chavanis, Phys. Rev. E 69, 066109 (2004)
P.H. Chavanis, C. Sire, Phys. Rev. E 70, 026115 (2004)
P.H. Chavanis, C. Sire, Phys. Rev. E 69, 016116 (2004)
P.H. Chavanis, e-print [arXiv: physics/0607020]
C. Sire, P.H. Chavanis Phys. Rev. E 61, 6644 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chavanis, P. Jeans type instability for a chemotactic model of cellular aggregation. Eur. Phys. J. B 52, 433–443 (2006). https://doi.org/10.1140/epjb/e2006-00310-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00310-y