Opinion dynamics is an important and very active area of research that delves into the complex processes through which individuals form and modify their opinions within a social context. The ability to comprehend and unravel the mechanisms that drive opinion formation is of great significance for predicting a wide range of social phenomena such as political polarization, the diffusion of misinformation, the formation of public consensus, and the emergence of collective behaviors. In this paper, we aim to contribute to that field by introducing a novel mathematical model that specifically accounts for the influence of social media networks on opinion dynamics. With the rise of platforms such as Twitter, Facebook, and Instagram and many others, social networks have become significant arenas where opinions are shared, discussed, and potentially altered. To this aim after an analytical construction of our new model and through incorporation of real-life data from Twitter, we calibrate the model parameters to accurately reflect the dynamics that unfold in social media, showing in particular the role played by the so-called influencers in driving individual opinions towards predetermined directions.

翻译：观点动力学是一个重要且活跃的研究领域，深入探索个体在社会环境中形成和改变观点的复杂过程。理解并揭示驱动观点形成的机制，对于预测政治极化、错误信息传播、公众共识形成及集体行为涌现等广泛社会现象具有重要意义。本文旨在通过引入一个专门考虑社交媒体网络对观点动力学影响的新型数学模型，为该领域做出贡献。随着推特、脸书和Instagram等平台的兴起，社交网络已成为观点分享、讨论和潜在改变的重要场域。为此，我们在对新模型进行分析性构建后，通过整合来自推特的真实数据，对模型参数进行校准以准确反映社交媒体中的动态变化，特别揭示了所谓"影响者"在引导个体观点朝向预定方向所发挥的作用。