标题： 社会活动驱动的意见动力学Kinetic模型的控制策略与平衡趋势 显示英文标题

标题： Control strategies and trends to equilibrium for kinetic models of opinion dynamics driven by social activity

摘要： 我们引入了新的 kinetic 方程来模拟人群中个体的意见动态，其中个体之间的互动倾向通过其社会活动水平来描述。 我们证明，在低活动水平的代理之间可能会出现意见极化，而活跃的代理则会达成共识，这突显了社会互动在防止极端意见形成中的重要性。 此外，我们提出了一种现实的控制策略，旨在减少非活动代理的数量并增加社会活跃代理的数量。 最后，我们对这种受控模型证明了几种（弱和强）收敛到平衡的结果。 特别是，通过考虑个人与能够引导人群平均意见的意见领袖之间的额外互动，我们使用类似熵方法的技术来估计解向平衡的松弛，这些解满足由具有时变系数的Wright-Fisher型模型给出的Fokker-Planck方程的伴随问题。 显示英文摘要

摘要： We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among agents with a low activity level, while active ones develop a consensus, highlighting the importance of social interactions to prevent the formation of extreme opinions. Moreover, we present a realistic control strategy aimed at reducing the number of inactive agents and increasing the number of socially active ones. At last, we prove several (weak and strong) convergence to equilibrium results for such controlled model. In particular, by considering additional interactions between individuals and opinion leaders capable of steering the average opinion of the population, we use entropy method-like techniques to estimate the relaxation toward equilibrium of solutions to a Fokker-Planck equation with adjoint given by a Wright-Fisher-type model with time-dependent coefficients.