Flocking dynamics mediated by weighted social networks

TL;DR

This paper investigates how weighted social networks influence flocking behavior in animal groups, revealing phases of ordered and disordered states, and demonstrating how weights affect the resilience and fragility of collective motion.

Contribution

It introduces a phase diagram for flocking transitions considering weighted networks and extends findings to realistic animal social networks and the Vicsek model.

Findings

Weighted networks can suppress or promote flocking transitions.

Presence of a maximum threshold for noise resilience depending on weight configurations.

Weights generally decrease flocking thresholds, increasing fragility.

Abstract

We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional substrate, application of a heterogeneous mean-field theory provides a phase diagram as function of the heterogeneity of the network connections and the correlations between weights and degree. In this diagram we observe two phases, one corresponding to the presence of a transition and other to a transition suppressed in an always ordered system, already observed in the non-weighted case. Interestingly, a third phase, with no transition in an always disordered state, is also obtained. These predictions, numerically recovered in computer simulations, are also fulfilled for the more realistic Vicsek model, with movement in a two-dimensional space. Additionally, we observe at finite network sizes the presence of a maximum threshold for particular weight configurations, indicating that it is possible to tune weights to achieve a maximum resilience to noise effects. Simulations in real weighted animal social networks show that, in general, the presence of weights diminishes the value of the flocking threshold, thus increasing the fragility of the flocking state. The shift in the threshold is observed to depend on the heterogeneity of the weight pattern.