AI 中文总结
提出选择性媒体影响下图子和现实世界网络的意见动态动力学模型，用模型预测控制策略，分析矩演化，导出方程并刻画稳态，通过实验研究相关参数及图子方法描述能力。
AI 中文摘要
我们提出了一种在基于图子和现实世界网络的选择性媒体影响下的意见动态动力学模型。受哈林球体理论启发的媒体行动通过一种模型预测控制策略纳入，该策略旨在引导主体的意见朝着期望的目标意见发展。对于由此产生的玻尔兹曼型描述，我们分析了矩的演化，并在准不变相互作用极限下，导出了一个福克 - 普朗克型方程及其稳态的特征。我们还证明了在傅里叶度量下到平衡的指数收敛。在由高斯图子生成的网络和现实世界的单问题推特网络上进行了数值实验，使我们能够研究控制和相互作用参数的作用，以及受媒体影响的主体子集的影响。利用现实世界社交网络数据初始化意见并推断相互作用结构，然后我们将在原始网络上获得的动态与由拟合其邻接矩阵的高斯图子产生的动态进行比较，从而评估图子方法对现实世界意见动态的描述能力。
英文摘要
We propose a kinetic model of opinion dynamics under selective media influence on both graphon-based and real-world networks. The media action, inspired by Hallin's theory of spheres, is incorporated through a model predictive control strategy designed to steer agents' opinions toward a desired target opinion. For the resulting Boltzmann-type description, we analyse the evolution of the moments and, in the quasi-invariant interaction limit, derive a Fokker--Planck-type equation together with a characterisation of its stationary states. We also prove exponential convergence to equilibrium in the Fourier metric. Numerical experiments are performed on networks generated by a Gaussian graphon and on real-world, single-issue Twitter networks, allowing us to investigate the role of control and interaction parameters, as well as the impact of the subset of agents subject to media influence. Using real-world social networks data to initialise opinions and infer the interaction structure, we then compare the dynamics obtained on the original networks with those produced by Gaussian graphons fitted to their adjacency matrices, thereby assessing the descriptive power of the graphon approach for real-world opinion dynamics.
Comments32 pages, 10 figures
