Dynamics of social contagions with heterogeneous adoption thresholds: Crossover phenomena in phase transition

TL;DR

This paper investigates how diverse adoption thresholds influence social contagion dynamics, revealing complex phase transition behaviors and crossover phenomena through a new theoretical model validated by simulations.

Contribution

It introduces a non-Markovian spreading threshold model with heterogeneous thresholds and develops an edge-based theory to analyze their effects.

Findings

Heterogeneous thresholds significantly impact final adoption size.

Multiple types of phase transitions are observed, including first-order, second-order, and hybrid.

Crossover phenomena occur, changing the nature of phase transitions based on threshold values.

Abstract

Heterogeneous adoption thresholds exist widely in social contagions, but were always neglected in previous studies. We first propose a non-Markovian spreading threshold model with general adoption threshold distribution. In order to understand the effects of heterogeneous adoption thresholds quantitatively, an edge-based compartmental theory is developed for the proposed model. We use a binary spreading threshold model as a specific example, in which some individuals have a low adoption threshold (i.e., activists) while the remaining ones hold a relatively high adoption threshold (i.e., bigots), to demonstrate that heterogeneous adoption thresholds markedly affect the final adoption size and phase transition. Interestingly, the first-order, second-order and hybrid phase transitions can be found in the system. More importantly, there are two different kinds of crossover phenomena in phase transition for distinct values of bigots' adoption threshold: a change from first-order or hybrid phase transition to the second-order phase transition. The theoretical predictions based on the suggested theory agree very well with the results of numerical simulations.