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arXiv · 1508.02809

Identifying manifolds underlying group motion in Vicsek agents

Kelum Gajamannage·Sachit Butail·Maurizio Porfiri·Erik M. Bollt
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Abstract

Collective motion of animal groups often undergoes changes due to perturbations. In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents. To characterize such manifolds, first we introduce a simple mapping of agents between time-steps. Then, we construct a novel metric which is susceptible to variations in the collective motion, thus revealing distinct underlying manifolds. The method is validated through three sample scenarios simulated using a Vicsek model, namely switching of speed, coordination, and structure of a group. Combined with a dimensionality reduction technique that is used to infer the dimensionality of the embedding manifold, this approach provides an effective model-free framework for the analysis of collective behavior across animal species.

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Kelum Gajamannage, Sachit Butail, Maurizio Porfiri, Erik M. Bollt. 2015-08-12. Identifying manifolds underlying group motion in Vicsek agents. https://doi.org/10.1140/epjst%2Fe2015-50088-2

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