Effects of long-range links on metastable states in a dynamic interaction network

Abstract

We introduce a model for random-walking agents on a two-dimensional periodic lattice, where the dynamic interaction network is defined using local short-range interactions and E randomly added long-range interactions. With periodic states for agents and an interaction rule of repeated averaging, we numerically find two types of metastable states at low- and high-E limits, respectively, along with consensus states. If we apply this model to opinion dynamics, metastable states can be interpreted as sustainable diversities in our societies, and our results then imply that, while diversities decrease and eventually disappear with more long-range interactions, other types of diverse states can appear under this rule when networks are almost fully connected.

Bootstrap percolation on spatial networks

“…Bootstrap percolation has found applications in modeling the spreading of information [17], the propagation of infection [18], the adoption of new products and social behaviors [19,20,21,22,23] such as trends, fads, political opinions, belief, rumors, innovations and financial decisions. For instance, one may decide to buy a product when recommended by more than k users and trust a message when told by at least k neighbors; cf.…”

“…Bootstrap percolation has found applications in explaining many important social phenomena, such as the spreading of information 12 , the propagation of infection 13 14 , the adoption of new products and social behaviors 15 16 17 18 including trends, fads, political opinions, belief, rumors, innovations and financial decisions. For instance, in emergence of cultural fads and adoption of new technology or objects, an individual can be positively influenced when there is a sufficient number of its close friends who have also done so 19 .…”