title: Influence of the number of topologically interacting neighbors on swarm dynamics.
abstract: Recent empirical and theoretical works on collective behaviors based on a topological interaction are beginning to offer some explanations as for the physical reasons behind the selection of a particular number of nearest neighbors locally affecting each individual's dynamics. Recently, flocking starlings have been shown to topologically interact with a very specific number of neighbors, between six to eight, while metric-free interactions were found to govern human crowd dynamics. Here, we use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study how the consensus reaching process and its dynamics are influenced by the number k of topological neighbors. Specifically, we prove exactly that, in the absence of noise, consensus is always attained with a speed to consensus strictly increasing with k. The analysis of both speed and time to consensus reveals that, irrespective of the swarm size, a value of k ~ 10 speeds up the rate of convergence to consensus to levels close to the one of the optimal all-to-all interaction signaling. Furthermore, this effect is found to be more pronounced in the presence of environmental noise.
authors.affiliation: Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682.
authors.forename: Yilun
authors.initials: Y
authors.lastname: Shang
authors.affiliation: Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682.
authors.forename: Roland
authors.initials: R
authors.lastname: Bouffanais
mesh_terms: D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D011153:Population