Dynamics of social contagions with local trend imitation

TL;DR

This paper introduces a social contagion model incorporating local trend imitation with a tent-like adoption probability, revealing how LTI strength influences phase transitions and maximizing behavior adoption.

Contribution

It presents a novel model with a generalized edge-based theory to analyze the impact of local trend imitation on social contagion dynamics.

Findings

Strong LTI leads to second-order phase transition.

Weak LTI results in first-order phase transition.

An optimal LTI capacity maximizes behavior adoption.

Abstract

Research on social contagion dynamics has not yet including a theoretical analysis of the ubiquitous local trend imitation (LTI) characteristic. We propose a social contagion model with a tent-like adoption probability distribution to investigate the effect of this LTI characteristic on behavior spreading. We also propose a generalized edge-based compartmental theory to describe the proposed model. Through extensive numerical simulations and theoretical analyses, we find a crossover in the phase transition: when the LTI capacity is strong, the growth of the final behavior adoption size exhibits a second-order phase transition. When the LTI capacity is weak, we see a first-order phase transition. For a given behavioral information transmission probability, there is an optimal LTI capacity that maximizes the final behavior adoption size. Finally we find that the above phenomena are not qualitatively affected by the heterogeneous degree distribution. Our suggested theory agrees with the simulation results.