Opinion Dynamics Considering Matthew Effect With Time Delays and Stubborn Influence in Social Networks

In social networks, stubborn individuals are resistant to changing their opinions or positions, affecting the trend of opinion evolution. Communication among individuals inherently involves time delays, which could lead to instability in information dissemination between individuals. To address these gaps in existing works, a new Matthew effect with time delays and stubborn influence (METS) model is proposed. In this paper, stubbornness coefficients are introduced to quantify individuals' adherence to their initial opinions, and a new approach to assess the speed of opinion development is proposed. Additionally, the social network is modeled as a distributed communication system that incorporates time delays to depict the connections between opinions. Furthermore, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-winners-take-all (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-WTA) operation is employed as the feedback mechanism of the model to differentiate the winners and losers within the Matthew effect. Then, a thorough analysis of the model's convergence and stability is provided. Besides, numerical experiments demonstrate the flexibility and practicality of the METS model. Finally, extensive simulations are conducted to examine the influence of individual stubbornness on the dynamics of opinion evolution.