Flocking dynamics mediated by weighted social networks

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.

12 pages, 9 figures

References in corpus (12)

• Novel type of phase transition in a system of self-driven particles
• Critical phenomena in complex networks
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Voter models on weighted networks
• Critical noise of majority-vote model on complex networks
• Zero temperature Glauber dynamics on complex networks
• On the numerical study of percolation and epidemic critical properties in networks
• Quenched mean-field theory for the majority-vote model on complex networks
• Scalar model of flocking dynamics on complex social networks
• Phase transitions on a class of generalized Vicsek-like models of collective motion