The Pattern Dynamics of Propagation Models in Complex Networks.

Area of Science:

• Complex Systems
• Network Science
• Mathematical Modeling

Background:

• Network rumors have detrimental impacts, necessitating effective control strategies.
• Traditional rumor propagation models often focus on physical space, overlooking cyberspace dynamics.
• Understanding pattern formation, like Turing instability, is crucial for analyzing complex network phenomena.

Purpose of the Study:

• To develop a rumor propagation model extending from physical to cyberspace using Laplacian matrices.
• To analyze the conditions for Turing instability in homogeneous and heterogeneous networks.
• To investigate the effectiveness of rumor control strategies by targeting key nodes and network layers.

Main Methods:

• Employing the Laplacian matrix to reconstruct a diffusion term for the rumor propagation model.
• Analyzing the occurrence conditions for Turing instability in various network structures (homogeneous and heterogeneous).
• Conducting numerical simulations to demonstrate and explore Turing patterns.

Main Results:

• Confirmed the existence of Turing patterns in network rumor propagation.
• Identified the Barabási-Albert (BA) scale-free network as suitable for real-world rumor scenarios in homogeneous networks.
• Demonstrated that targeting key nodes or specific layers in heterogeneous networks is effective for rumor governance.

Conclusions:

• The developed model effectively captures rumor propagation dynamics in cyberspace.
• Targeted interventions, such as focusing on key nodes or layers, offer efficient rumor control strategies.
• Network structure significantly influences rumor spread and control, with scale-free networks showing real-world applicability.