Emotional Contagion in Physical–Cyber Integrated Networks: The Phase Transition Perspective

Understanding the emotional contagion process in the crowd will help to take measures in advance to avoid the large-scale spread of negative emotions in emergencies and reduce the loss of lives and properties. Studying the phase transition phenomenon is fundamental to analyzing and evaluating the crowd emotional contagion. However, it is a challenging issue since most people participate in both the physical and cyber networks at the same time. In this article, we focus on the emotional contagion in physical–cyber integrated networks from the phase transition perspective. To achieve this, we first construct a physical–cyber integrated network model to describe the interactions between physical and cyber networks. Second, we build an emotional contagion model to capture the characteristics of emotional contagion in the physical and cyber integrated networks accurately. Finally, we study the phase transition phenomenon of emotional contagion and identify the critical threshold by mapping the emotional contagion to the joint site/bond percolation model. Numerical simulations and experiments further support and enrich our conclusions. The proposed method is expected to provide guidance for controlling emotional contagion in emergencies.