Emergence of hysteresis loop in social contagions on complex networks

Zhen Su,H Eugene Stanley,Lixiang Li,Wei Wang,Jinghua Xiao

doi:10.1038/s41598-017-06286-w

Abstract

Understanding the spreading mechanisms of social contagions in complex network systems has attracted much attention in the physics community. Here we propose a generalized threshold model to describe social contagions. Using extensive numerical simulations and theoretical analyses, we find that a hysteresis loop emerges in the system. Specifically, the steady state of the system is sensitive to the initial conditions of the dynamics of the system. In the steady state, the adoption size increases discontinuously with the transmission probability of information about social contagions, and trial size exhibits a non-monotonic pattern, i.e., it first increases discontinuously then decreases continuously. Finally we study social contagions on heterogeneous networks and find that network topology does not qualitatively affect our results.

Highlights

Social contagion processes are everywhere range from the spread of health behavior to the diffusion of new products and the spread of innovation1–5
In this paper we propose a susceptible-trial-adopted-susceptible (STAS) model to investigate social contagions on complex networks in which an individual in the susceptible state passes through a trial state prior to reaching the adopted state or directly reaches the adopted state
We propose a generalized susceptible-trial-adopted-susceptible (STAS) threshold model19 to investigate social contagions in uncorrelated complex networks

Summary

Introduction

Social contagion processes are everywhere range from the spread of health behavior to the diffusion of new products and the spread of innovation. Many successful models for revealing spreading mechanisms have been proposed, and they have found that dynamic processes and critical phenomena are affected by both spreading mechanisms and network topologies7, 9–11 Among these spreading mechanisms, social reinforcement plays an important role in social contagions (e.g., the spread of a behavior) but does not exist in biological contagion (e.g., the spread of a disease). Using extensive simulations and percolation theory, Watts found that social reinforcement causes the fraction of nodes in the active state versus the average degree to first increase continuously and decrease discontinuously Majdandzic and his colleagues found that social reinforcement induces a phase flipping (i.e., hysteresis loop) phenomena that explains some phenomena in real economic networks . We find that heterogeneity does not qualitatively affect the results

Methods

Results

Conclusion