Динамика ансамбля активных броуновских частиц, управляемых шумом

Математическая биология и биоинформатика. 2015;10(1):72-87.

doi: 10.17537/2015.10.72.

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. doi: 10.1140/epjst/e2012-01529-y
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. 1998;80:5044-5047. doi: 10.1103/PhysRevLett.80.5044
4. Ebeling W, Schweitzer F, Tilch B. Active Brownian particles with energy depots modeling animal mobility. Biosystems. 1999;49:17-29. doi: 10.1016/S0303-2647(98)00027-6
5. Erdman U, Ebeling W, Schimansky-Geier L, Schweitzer F. Brownian particles far from equilibrium. Eur. Phys. J. B. 2000. V. B15:105-113.
6. Ebeling W, Schimansky-Geier L, Romanovsky Yu. Stochastic Dynamics of Reacting Biomolecules. Singapore: World Scientific; 2002.
7. Schweitzer F. Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences. Berlin: Springer; 2003.
8. Chetverikov A, Ebeling W, Velarde MG. Thermodynamic and phase transitions in dissipative and active Morse chain. Eur. Phis. J. 2005;44:509-519.
9. Chetverikov AP, Ebeling W, Velarde MG. Solitons and clusters in one-dimensional ensembles of interacting Brownian particles. Izvestiia Saratovskogo universiteta. Seriia fizika (Izvestiya of Saratov University. Series Physics). 2006;6(1/2):28-41 (in Russ.).
10. Schienbein M, Gruler H. Langevin equation, Fokker-Planck equation and cell migration. Bull. Math. Biol. 1993. 55(3):585-608. doi: 10.1007/BF02460652
11. Romanczuk P, Erdmann U. Collective motion of active Brownian particles in one dimension. Eur. Phys. J. Special Topics. 2010;187:127-134.
12. Romanczuk P, Schimansky-Geier L. Mean-field theory of collective motion due to velocity alignment. Ecol. Complexity. 2012;10:82-92.
13. Sergeev KS, Vadivasova TE, Chetverikov AP. Noise-induced transition in a small ensemble of active Brownian particles. Technical Physics Letters. 2014;40(11):976-979. doi: 10.1134/S1063785014110108
14. Arnold L. Random Dynamical Systems. Berlin: Springer; 2003.
15. Nikitin NN, Razevig VD. Methods for the digital simulation of stochastic differential equations and an estimate of their errors. Zh. Vychisl. Mat. Mat. Fiz. 1978;18(1):106-117 (in Russ.).