Dynamics of social contagions with memory of non-redundant information

TL;DR

This paper introduces a new social contagion model incorporating non-redundant information memory, revealing how memory influences adoption dynamics and causes phase transitions in social behavior spread.

Contribution

It develops a unified edge-based theory for social contagion with reinforcement from non-redundant information, and demonstrates how memory affects the final adoption size and transition phenomena.

Findings

Memory significantly impacts the spread dynamics.

Transition from discontinuous to continuous adoption size dependence.

System parameters can trigger phase transitions.

Abstract

A key ingredient in social contagion dynamics is reinforcement, as adopting a certain social behavior requires verification of its credibility and legitimacy. Memory of non-redundant information plays an important role in reinforcement, which so far has eluded theoretical analysis. We first propose a general social contagion model with reinforcement derived from non-redundant information memory. Then, we develop a unified edge-based compartmental theory to analyze this model, and a remarkable agreement with numerics is obtained on some specific models. Using a spreading threshold model as a specific example to understand the memory effect, in which each individual adopts a social behavior only when the cumulative pieces of information that the individual received from his/her neighbors exceeds an adoption threshold. Through analysis and numerical simulations, we find that the memory characteristic markedly affects the dynamics as quantified by the final adoption size. Strikingly, we uncover a transition phenomenon in which the dependence of the final adoption size on some key parameters, such as the transmission probability, can change from being discontinuous to being continuous. The transition can be triggered by proper parameters and structural perturbations to the system, such as decreasing individuals' adoption threshold, increasing initial seed size, or enhancing the network heterogeneity.