Scalar model of flocking dynamics on complex social networks

TL;DR

This paper explores how long-range social interactions influence flocking behavior on complex networks, revealing that network heterogeneity significantly affects phase transition phenomena in collective motion models.

Contribution

It introduces a scalar model of flocking on complex social networks and analytically demonstrates how network heterogeneity alters phase transition behavior.

Findings

Low heterogeneity networks exhibit a phase transition between ordered and disordered states.

High heterogeneity networks suppress the phase transition, resulting in always ordered states.

Analytical solutions support the phenomenological observations.

Abstract

We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in several social species. In this scalar model we find a phenomenology analogous to that observed in the classic Vicsek model: In networks with low heterogeneity, a phase transition separates an ordered from a disordered phase. At high levels of heterogeneity, instead, the transition is suppressed and the system is always ordered. This observation is backed up analytically by the solution of a modified scalar model within an heterogeneous mean-field approximation. Our work extends the understanding of the effects of social interactions in flocking dynamics and opens the path to the analytical study of more complex topologies of social ties.