The Pattern Dynamics of Propagation Models in Complex Networks.

Based on the detrimental impact of network rumors, we employ the Laplacian matrix to reconstruct a diffusion term and establish a rumor propagation model that extends from traditional physical space to cyberspace. In this paper, we analyze the occurrence conditions for Turing instability in both homogeneous and heterogeneous networks and generalize the necessary conditions for Turing instability in higher-order systems. Through numerical simulations, we demonstrate the existence of Turing patterns. Additionally, we explore the intricate nature of Turing patterns within various network structures. The findings from the homogeneous network indicate that the BA scale-free network is better suited for real-world scenarios. When implementing rumor-refuting policies, prioritizing individuals in key nodes can effectively control rumors throughout the entire network, significantly enhancing rumor control efficiency. The results on heterogeneous networks demonstrate that altering the key layer instead of modifying the entire three-layer network structure can also achieve the goal of rumor governance. This discovery substantially reduces the complexity associated with rumor control.