Brunet-Derrida particle systems


This is a branching-selection system in the real line with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. The dynamics give rise to a cloud of particles moving to the right. The simulation shows the tail distribution of the resulting process, which appears to have a traveling wave solution behavior. For more details see the paper.

Here is a movie of the simulation, where the initial condition is a superposition of two Gaussians.
Note: the apparent increase in the speed of propagation as the distribution becomes roughly unimodal has to do with the fact that the simulation runs faster after that and the speed of the movie has not been adjusted accordingly. It is most likely not a feature of the model.
Traveling wave

Python source code: bd.tar.gz

Last modified: September 2010

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