Flocking: Influence of Metric Versus Topological Interactions

TL;DR

This study compares metric and topological interaction rules in flocking models, revealing that topological interactions more effectively induce ordered collective motion, with thresholds identified for both interaction types.

Contribution

It provides a systematic analysis of how interaction range and number of neighbors influence flocking dynamics, highlighting the superiority of topological interactions in achieving order.

Findings

Topological interactions lead to more effective flock ordering.

Thresholds exist for interaction radius and neighbor count to achieve order.

Topological rules outperform metric rules in natural flocking scenarios.

Abstract

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated over in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; in contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.