The European Physical Journal Special Topics

, Volume 224, Issue 17–18, pp 3245–3256 | Cite as

Identifying manifolds underlying group motion in Vicsek agents

  • K. GajamannageEmail author
  • S. ButailEmail author
  • M. PorfiriEmail author
  • E.M. BolltEmail author
Regular Article Physics of Social Interactions
Part of the following topical collections:
  1. Dynamics of Animal Systems


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.


Manifold European Physical Journal Special Topic Collective Behavior Collective Motion Group Speed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Department of MathematicsClarkson University, PotsdamNew YorkUSA
  2. 2.Indraprastha Institute of Information Technology DelhiNew DelhiIndia
  3. 3.Department of Mechanical and Aerospace EngineeringNew York UniversityNew YorkUSA

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