Information transfer in finite flocks with topological interactions

The Vicsek model is a flocking model comprising simple point particles originally proposed with metric interactions: particles align to neighbours within a radius. Later, topological interactions were introduced such that particles align with their closest k neighbours. 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 particle aligns with its neighbours, and the flock direction. These quantities have been shown to be important in characterising phases transitions, such as that exhibited by the Vicsek model. 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 transfer for the ordered regime, the topological model maintains this maximal information transfer dependent on noise and velocity, rather than the current phase.