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.

The Influences of Self-Introspection and Credit Evaluation on Self-Organized Flocking

“…Individual heterogeneity represented by nodes with different properties can affect collective behavior, and previous studies have shown that collective systems with heterogeneous individuals can improve the performance of collective motion [26][27][28]. Similarly, from the perspective of complex networks [29,30], social interaction represented by edges between nodes is also heterogeneous; that is, there are differences in interaction mechanisms [31], which also conform to real biological behavior. Some research on theoretical modeling considers that the interaction behavior between individuals and neighbors should be variable with time [32].…”