The European Physical Journal Special Topics

, Volume 187, Issue 1, pp 127–134 | Cite as

Collective motion of active Brownian particles in one dimension

  • P. Romanczuk
  • U. Erdmann


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.


European Physical Journal Special Topic Noise Intensity Collective Motion Moment Equation Nonlinear Stochastic System 
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© EDP Sciences and Springer 2010

Authors and Affiliations

  1. 1.Department of PhysicsHumboldt Universität zu BerlinBerlinGermany
  2. 2.Helmholtz Association of German Research CentresBerlinGermany

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