seminar: Spatial Instabilities and Size Limitations of Flocks
speaker: Peter Veerman (Portland State University)abstract: The movement of flocks with a leader can be stabilized over time as has been shown before. But for large flocks perturbations in the movement of the leader may nonetheless grow to a considerable size as they propagate throughout the flock and before they die out over time. We calculate the effect of this "finite size resonance" and indicate two applications of these ideas. The first is that if perturbations grow as the size of the flock gets larger, then the size of the flock will have a natural limitation. It turns out that for flocks with a symmetric communication graph perturbations grow much slower than in the asymmetric case. This enables agents who sense equally well in all directions to form much larger flocks than ones who don't.
The second application concerns a simple traffic-like problem. Suppose the leader accelerates from standstill to a given velocity and a large flock is supposed to follow it. The acceleration of the leader is the `perturbation'. How does the perturbation propagate, and what is the maximum size of the flock that can be safely `led' by a single leader?
timetable:
Fri 6 Apr, 10:00 - 10:30, Aula Dini
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