Information propagation dynamics on heterogeneous-homogeneous coupling bi-layer networks.

The proliferation of multi-platform network information has expanded communication channels for users, enabling the integration and dissemination of information across both Social Networking Services (SNS)-type app and Instant Message (IM)-type app. With the intensification of convergent communication, some users in the two types of apps show active alternation in spreading information to each other's platforms. The study of the evolution trend of information in different platforms is of great practical significance for the mastery of the communication law. This study synthesizes the following three points: (1) The information in SNS-type app diffuses from key nodes with more followers to ordinary nodes, showing the characteristics of heterogeneous network with radial and explosive propagation. (2) The information in IM-type app mainly depends on the "relationship chain" diffusion, showing the characteristics of homogeneous network with gradual and multi-cluster propagation. (3) SNS-type apps and IM-type apps with some users showing coupled propagation characteristics. Therefore, this study constructs the heterogeneous-homogeneous asymmetric coupling two-layer network information propagation dynamics model. The propagation threshold R0 and the stability of the model are derived theoretically. Real network data sets are used to simulate the platform fusion. Numerical simulations confirm the rationality of the propagation threshold and perform changes analyses of parameters, such as the degree of cross-circulation of platforms, users' tendency of multi-platform expression, and changes in users' behaviors towards information dissemination. Simulation results reveal that promoting platform integration can improve communication efficiency in the real world. Dual-platform communication by IM-platform spreaders substantially contributes to the growth in the number of SNS-platform spreaders. The higher the level of disinterest in dual-platform spreaders, the more likely it is to inhibit the growth of spreaders and removers, with IM-type app demonstrating more pronounced effects.