Collective motion of active Brownian particles in one dimension
1 Department of Physics, Humboldt Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
2 Helmholtz Association of German Research Centres, Anna-Louisa-Karsch-Straße 2, 10178 Berlin, Germany
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Revised: 9 August 2010
Published online: 1 October 2010
We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.
© EDP Sciences, Springer-Verlag, 2010