Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact

Abstract

In complex systems, individuals exhibit various social contact capacities on account of differences in societal strata, educational backgrounds, and individual psychology. It is a fact that people tend to utilize diverse social networks and demonstrate ever-changing fashion trends. From our study on personal psychology, we have noted that individuals display a behaviour known as dynamic fashion tendency (DFT) when receiving information. Next, to represent DFT behaviour through a threshold model, we devised a dynamic SAR propagation model on a multi-layer contact network. For the transmission mechanism of individual behaviour, we utilized partition theory to investigate and uncover. Both theoretical analysis and simulation experiments demonstrate that the propagation mode exhibits a boundary phenomenon. The final adoption size may demonstrate either continuous second-order or discontinuous first-order phase transitions, depending on individual DFT behaviour. When unit propagation probability is constant, the largest final adoption size is attained with the ideal DFT parameters. Additionally, personal contact plays a role in spreading behaviour and shifting the propagation pattern from continuous second-order to discontinuous first-order. Ultimately, numerical analysis can correspond with real models.