Geodesic
Dynamics of ensemble of active brownian particles controlled by noise
Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015) no. 1, pp. 72-87 
K. S. Sergeev; T. E. Vadivasova; A. P. Chetverikov. Dynamics of ensemble of active brownian particles controlled by noise. Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015) no. 1, pp. 72-87. http://geodesic.mathdoc.fr/item/MBB_2015_10_1_a7/
@article{MBB_2015_10_1_a7,
     author = {K. S. Sergeev and T. E. Vadivasova and A. P. Chetverikov},
     title = {Dynamics of ensemble of active brownian particles controlled by noise},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {72--87},
     year = {2015},
     volume = {10},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2015_10_1_a7/}
}
TY  - JOUR
AU  - K. S. Sergeev
AU  - T. E. Vadivasova
AU  - A. P. Chetverikov
TI  - Dynamics of ensemble of active brownian particles controlled by noise
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2015
SP  - 72
EP  - 87
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MBB_2015_10_1_a7/
LA  - ru
ID  - MBB_2015_10_1_a7
ER  - 
%0 Journal Article
%A K. S. Sergeev
%A T. E. Vadivasova
%A A. P. Chetverikov
%T Dynamics of ensemble of active brownian particles controlled by noise
%J Matematičeskaâ biologiâ i bioinformatika
%D 2015
%P 72-87
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/MBB_2015_10_1_a7/
%G ru
%F MBB_2015_10_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

Dynamics of an ensemble of small number of active Brownian particles is studied by means of numerical simulations. The particles are influenced by independent sources of noise, passive and active, and interact with each other through a global velocity field. We suppose that active noise affects to direction of the particle velocity only. Behaviour of the large ensemble and behaviour of the small one are compared. Mean velocity of particles of the large ensemble was analytically estimated earler. We show that a noise-induced "order–disorder" transition accompaniated by a bistability phenomena is observed in a small ensemble. A borderline of a coupling coefficient moves up while reducing the number of particles. Influence of passive noise leads to conversion of bistability to bimodality. There are two most probable values of a particle velocity in the last case. Borders of regions of bistability and bimodality are defined by the stochastic bifurcations of different kinds.

[1] Romanczuk P., Bar M., Ebeling W., Lindner B., Schimansky-Geier L., “Active Brownian particles: From individual to collective stochastic dynamics”, Eur. Phys. J. Special Topics, 2012

[2] Großmann R., Schimansky-Geier L., Romanczuk P., “Active Brownian particles and active fluctuations with velocity-alignment”, New Journal of Physics, 2012

[3] Schweitzer F., Ebeling W., Tilch B., “Complex motion of Brownian particles with energy depots”, Phys. Rev. Lett., 80 (1998), 5044–5047 | DOI

[4] Ebeling W., Schweitzer F., Tilch B., “Active Brownian particles with energy depots modeling animal mobility”, Biosystems, 49 (1999), 17–29 | DOI

[5] Erdman U., Ebeling W., Schimansky-Geier L., Schweitzer F., “Brownian particles far from equilibrium”, Eur. Phys. J. B, B15 (2000), 105–113 | DOI

[6] Ebeling W., Schimansky-Geier L., Romanovsky Yu., Stochastic Dynamics of Reacting Biomolecules, World Scientific, Singapore, 2002

[7] Schweitzer F., Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences, Springer, Berlin, 2003 | MR

[8] Chetverikov A., Ebeling W., Velarde M. G., “Thermodynamic and phase transitions in dissipative and active Morse chain”, Eur. Phys. J. B, 44 (2005), 509–519 | DOI

[9] Chetverikov A. P., Ebeling V., Velarde M. G., “Solitony i klastery v odnomernykh ansamblyakh vzaimodeistvuyuschikh brounovskikh chastits”, Izvestiya Saratovskogo universiteta. Seriya Fizika, 6:1/2 (2006), 28–41 | MR

[10] Schienbein M., Gruler H., “Langevin equation, Fokker–Planck equation and cell migration”, Bull. Math. Biol., 55:3 (1993), 585–608 | DOI

[11] Romanczuk P., Erdmann U., “Collective motion of active Brownian particles in one dimension”, Eur. Phys. J. Special Topics, 187 (2010), 127–134 | DOI

[12] Romanczuk P., Schimansky-Geier L., “Mean-field theory of collective motion due to velocity alignment”, Ecol. Complexity, 10 (2012), 82–92 | DOI

[13] Sergeev K. S., Vadivasova T. E., Chetverikov A. P., “Indutsirovannyi shumom perekhod v malom ansamble aktivnykh brounovskikh chastits”, Pisma v ZhTF, 40:21 (2014), 88–96

[14] Arnold L., Random Dynamical Systems, Springer, Berlin, 2003 | MR

[15] Nikitin N. N., Razevig V. D., “Metody tsifrovogo modelirovaniya stokhasticheskikh differentsialnykh uravnenii i otsenka ikh pogreshnostei”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 18:1 (1978), 107