Interacting Social Processes on Interconnected Networks.

Lucila G Alvarez-Zuzek,Cristian E La Rocca,Federico Vazquez,Lidia A Braunstein,Peter Csermely

doi:10.1371/journal.pone.0163593

Abstract

We propose and study a model for the interplay between two different dynamical processes –one for opinion formation and the other for decision making– on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = −2,−1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = −1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r*(β), while a negative consensus happens for r < r*(β). In the r − β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β < βc to a dominance of one orientation for β > βc. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r*, β*).

Highlights

The study of complex networks has become a matter of great interest to scientists, due to the large number of real systems that evolve on top of these kind of topological structures, such as human societies, climate, transportation and physiological systems
Because we were interested in studying whether the dynamics in network A prevails over the dynamics in network B, we run many independent realizations of the dynamics and calculated the probability P+ that the entire two-network system reaches a + consensus, that is, the initial orientation adopted by network A
We study a system that consists of two interconnected networks A and B, where an AS dynamics with fixed volatility α = βÃ runs on network A, and another AS dynamics with variable volatility β runs on network B

Summary

Introduction

The study of complex networks has become a matter of great interest to scientists, due to the large number of real systems that evolve on top of these kind of topological structures, such as human societies, climate, transportation and physiological systems. In this article we investigate the interaction between two social dynamics, one for opinion formation and the other for decision making, that take place on two interconnected networks. The dynamics for opinion formation corresponds to that of the model proposed by La Rocca et al [42], to which we refer as the M-model This model possesses 2M different states describing the spectrum of possible opinion orientations on a given issue, from totally against (state S = −M) to totally in favor (S = M), with some moderate opinions between these extreme values. We set the system to explore a hypothetical polarized scenario where, initially, all the agents in the opinion network are in favor of the issue (positive orientations), while all the agents in the decision network are against (negative orientations) By means of this simple model we address the following questions: under which conditions the opinion dynamics is able to influence and reverse the initial orientation of the decision network?

The Model

Simulation Results

Mean Field Approach

Discussion