J. Adler, Chemotaxis in Bacteria, Science, vol.153, issue.3737, pp.708-716, 1966.
DOI : 10.1126/science.153.3737.708

E. O. Budrene and H. C. Berg, Complex patterns formed by motile cells of Escherichia coli, Nature, vol.349, issue.6310, p.630, 1991.
DOI : 10.1038/349630a0

E. O. Budrene and H. C. Berg, Dynamics of formation of symmetrical patterns by chemotactic bacteria, Nature, vol.376, issue.6535, p.49, 1995.
DOI : 10.1038/376049a0

C. Liu, X. Fu, L. Liu, X. Ren, C. K. Chau et al., Sequential Establishment of Stripe Patterns in an Expanding Cell Population, Science, vol.20, issue.2, pp.238-241, 2011.
DOI : 10.1038/2417

E. F. Keller and L. A. Segel, Model for chemotaxis, Journal of Theoretical Biology, vol.30, issue.2, p.225, 1971.
DOI : 10.1016/0022-5193(71)90050-6

E. F. Keller and L. A. Segel, Traveling bands of chemotactic bacteria: A theoretical analysis, Journal of Theoretical Biology, vol.30, issue.2, p.235, 1971.
DOI : 10.1016/0022-5193(71)90051-8

M. J. Tindall, P. K. Maini, S. L. Porter, and J. P. Armitage, Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations, Bulletin of Mathematical Biology, vol.178, issue.6, pp.1570-1607, 2008.
DOI : 10.1016/0022-5193(75)90174-5

T. Hillen and K. J. Painter, A user???s guide to PDE models for chemotaxis, Journal of Mathematical Biology, vol.15, issue.1, pp.183-217, 2009.
DOI : 10.1007/BF02458292

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.228.2990

A. Chertock, A. Kurganov, X. Wang, and Y. Wu, On a chemotaxis model with saturated chemotactic flux, Kinetic and related models 5, pp.51-95, 2012.

N. Bellomo, A. Bellouquid, Y. Tao, and M. Winkler, Toward a mathematical theory of Keller???Segel models of pattern formation in biological tissues, Mathematical Models and Methods in Applied Sciences, vol.33, issue.09, pp.1663-1763, 2015.
DOI : 10.1016/j.jmaa.2014.11.031

N. Bellomo and M. Winkler, A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up, Communications in Partial Differential Equations, vol.44, issue.3, pp.436-473, 2017.
DOI : 10.1016/j.matpur.2013.01.020

S. M. Block, J. E. Segall, and H. C. Berg, Adaptation kinetics in bacterial chemotaxis, J. Bacteriol, vol.154, pp.312-323, 1983.

Y. Dolak and C. Schmeiser, Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms, Journal of Mathematical Biology, vol.23, issue.6, p.595, 2005.
DOI : 10.1099/00221287-85-2-321

J. Saragosti, V. Calvez, N. Bournaveas, B. Perthame, A. Buguin et al., Directional persistence of chemotactic bacteria in a traveling concentration wave, Proceedings of the National Academy of Sciences, vol.151, issue.2, p.16235, 2011.
DOI : 10.1016/j.jsb.2005.06.002

URL : https://hal.archives-ouvertes.fr/hal-00789064

F. James and N. Vauchelet, Chemotaxis: from kinetic equations to aggregate dynamics, Nonlinear Differ, Equ. Appl, vol.20, p.101, 2013.
DOI : 10.1007/s00030-012-0155-4

URL : https://link.springer.com/content/pdf/10.1007%2Fs00030-012-0155-4.pdf

V. Calvez, Chemotactic waves of bacteria at the mesoscale, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01340375

B. Perthame, N. Vauchelet, and Z. Wang, Modulation of stiff response in E. coli Bacterial populations

P. K. Maini, M. R. Myerscough, K. H. Winters, and J. D. Murray, Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation, Bulletin of Mathematical Biology, vol.295, issue.5, pp.701-719, 1991.
DOI : 10.1007/978-3-662-08539-4

M. Mimura and T. Tsujikawa, Aggregating pattern dynamics in a chemotaxis model including growth, Physica A: Statistical Mechanics and its Applications, vol.230, issue.3-4, pp.499-543, 1996.
DOI : 10.1016/0378-4371(96)00051-9

K. J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D: Nonlinear Phenomena, vol.240, issue.4-5, pp.363-375, 2011.
DOI : 10.1016/j.physd.2010.09.011

S. Ei, H. Izuhara, and M. Mimura, Spatio-temporal oscillations in the Keller???Segel system with logistic growth, Physica D: Nonlinear Phenomena, vol.277, pp.1-21, 2014.
DOI : 10.1016/j.physd.2014.03.002

J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan et al., Mathematical Description of Bacterial Traveling Pulses, PLoS Computational Biology, vol.33, issue.8, p.1000890, 2010.
DOI : 10.1371/journal.pcbi.1000890.s001

URL : https://hal.archives-ouvertes.fr/hal-00440108

C. Emako, C. Gayrard, A. Buguin, L. Almeida, and N. Vauchelet, Traveling Pulses for a Two-Species Chemotaxis Model, PLOS Computational Biology, vol.97, issue.6, p.1004843, 2016.
DOI : 10.1371/journal.pcbi.1004843.t001

URL : https://hal.archives-ouvertes.fr/hal-01302632

B. Perthame, Parabolic equations in biology, 2015.
DOI : 10.1007/978-3-319-19500-1

URL : https://hal.archives-ouvertes.fr/hal-01423552

G. Nadin, B. Perthame, and L. Ryzhik, Traveling waves for the Keller-Segel system with Fisher birth terms, Interface free bound, pp.517-538, 2008.

G. Nadin, B. Perthame, and M. Tang, Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation, Comptes Rendus Mathematique, vol.349, issue.9-10, pp.349-553, 2011.
DOI : 10.1016/j.crma.2011.03.008

URL : https://hal.archives-ouvertes.fr/hal-00537986

B. Perthame and S. Yasuda, Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller-Segel equation

Y. V. Kalinin, L. Jiang, Y. Tu, and M. Wu, Logarithmic Sensing in Escherichia coli Bacterial Chemotaxis, Biophysical Journal, vol.96, issue.6, pp.2439-2448, 2009.
DOI : 10.1016/j.bpj.2008.10.027

URL : http://doi.org/10.1016/j.bpj.2008.10.027

R. A. Fisher, The advance of advantageous genes, pp.335-369, 1937.

A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piskunov, Etude de l'´ equation de la diffusion avec croissance de la quantité dematì re et son applicationàapplicationà unprobì eme biologique, Moskow. Univ. Math. Bull, vol.1, pp.1-25, 1937.

D. G. Aronson and H. F. Weinberger, Lecture notes in mathematics, 1975.