Various Vicsek Models with Underlying Network Characteristics

TL;DR

This paper investigates how different underlying network structures influence collective motion in Vicsek models, revealing that network topology and average degree critically affect synchronization in biological swarms.

Contribution

It introduces a network perspective to Vicsek models, showing how homogeneous and heterogeneous interactions form specific network types and impact synchronization.

Findings

Homogeneous interactions form Erdos-Renyi networks.

Heterogeneous interactions lead to Barabasi-Albert networks.

Synchronization correlates with the average degree of the network.

Abstract

Collective motion is a fundamental phenomenon in biological swarms. As a framework for studying synchronization in motions, the Vicsek model is simple and efficient, assuming isotropic interactions with a complete field of view. Drawing inspiration from natural swarms, we incorporate realistic constraints into the model. By analysing the interaction structures from the complex network perspective, we demonstrate that models with the homogeneous interaction rules naturally form Erdos-Renyi networks, whereas the introduction of heterogeneity leads to Barabasi-Albert networks. Furthermore, we discover that the model's synchronization is fundamentally governed by the average degree of the interaction network. Through a comparative analysis across these topologies, we identify a stretched-exponential relationship between the average degree and the synchronization metrics.