Dynamics Modeling of Dual-Opinion Interaction and Propagation in Cross-Platform Coupled Social Networks

The increasing integration of social media platforms has transformed public opinion propagation into a nonlinear, cross-platform coupled process, posing challenges to traditional governance frameworks. This study proposes a novel interactive dual-opinion propagation model for cross-platform coupled networks, which integrates four key factors: opinion interaction, interlayer coupling strength, interlayer coupling patterns, and user social activity in activity-driven temporal regimes. Using an enhanced SEIR framework, we derive the spreading threshold analytically, showing that interlayer coupling reduces the threshold and amplifies cross-platform diffusion. Subsequently, we perform numerical simulations to explore the factors influencing dual-opinion propagation. Simulations reveal that opinion interaction asymmetrically influences propagation: the weaker opinion is highly sensitive to the interaction type, experiencing synergistic enhancement under positive correlation but suppression under negative correlation, whereas the stronger opinion remains robust. In static networks, propagation is dominated by fixed coupling strength, whereas in activity-driven temporal networks, it is co-determined by initial coupling density and dynamic user activity, with the sparse layer exhibiting high sensitivity to both coupling strength and internal activity levels. This work provides a realistic analytical framework for opinion dynamics in coupled social ecosystems and offers actionable insights for cross-platform public opinion governance.