Eur. Phys. J. Special Topics 224, 3245-3256 (2015)
https://doi.org/10.1140/epjst/e2015-50088-2

Regular Article

Identifying manifolds underlying group motion in Vicsek agents

¹ Department of Mathematics, Clarkson University, Potsdam, New York, USA
² Indraprastha Institute of Information Technology Delhi, New Delhi, India
³ Department of Mechanical and Aerospace Engineering, New York University, Brooklyn, New York, USA

^a e-mail: dineshhk@clarkson.edu
^b e-mail: sbutail@iiitd.ac.in
^c e-mail: mporfiri@nyu.edu
^d e-mail: ebollt@clarkson.edu

Received: 20 April 2015
Revised: 2 November 2015
Published online: 15 December 2015

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.