ABSTRACT
The convergence time for flocking in the Vicsek-Cucker-Smale model is known to be bounded by a tower-of-twos of height linear in the number of birds. We improve the height to logarithmic, which matches the known lower bound. In the process, we introduce an intriguing geometric object, the "flight net", and develop the idea of a "virtual agent." These two concepts give us insight into early flocking behavior, which is still the most mysterious aspect of these dynamical systems.
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Index Terms
- The geometry of flocking
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