Information Flow in Finite Flocks with Topological Interactions

TL;DR

This paper investigates information flow in finite flocks with topological interactions using simulations of the Vicsek model, revealing how information theoretic measures depend on observation time and differ from metric models.

Contribution

It introduces a topological interaction variant of the Vicsek model and analyzes how information flow measures behave, highlighting differences from traditional metric-based models.

Findings

Information measures depend on observation time.

Topological model converges faster to long-term behavior.

Maximal information flow persists beyond phase transition in topological model.

Abstract

We simulate the Vicsek model utilising topological neighbour interactions and estimate information theoretic quantities as a function of noise, the variability in the extent to which each animal aligns with its neighbours, and the flock direction. We show that these quantities, mutual information and global transfer entropy, are in fact dependent on observation time, and in comparison to the canonical Vicsek model which utilises range-based interactions, the topological variant converges to the long-term limiting behaviour with smaller observation windows. Finally, we show that in contrast to the metric model, which exhibits maximal information flow for the ordered regime, the topological model maintains this maximal information flow beyond the phase transition and into the disordered regime.