论文标题
羊毛毛毛毛毛衣系统和动态意见游戏的减少
Grassmannian reduction of Cucker-Smale systems and dynamical opinion games
论文作者
论文摘要
在本说明中，我们研究了具有自我推测和瑞利型摩擦力的新一类对齐模型，该模型描述了具有个体特征参数的代理的集体行为。我们通过一种新方法描述了长时间的动力学，该方法允许将分析从多维系统减少到由适当的grassmanian参数参数化的二维系统的更简单家族。通过这种方法，我们证明了一类大的（且清晰）的初始速度配置的指数对齐，仅限制在开放小于$π$的扇区的范围内。 在特征参数保持冷冻的情况下，该系统控制着一组有信念的参与者的观点动态。该系统被视为一种动态的非合作游戏，具有独特的稳定纳什均衡，这代表了所有代理人最令人愉快的观点。此外，这种协议被证明是任何初始意见的全球吸引者。
In this note we study a new class of alignment models with self-propulsion and Rayleigh-type friction forces, which describes the collective behavior of agents with individual characteristic parameters. We describe the long time dynamics via a new method which allows to reduce analysis from the multidimensional system to a simpler family of two-dimensional systems parametrized by a proper Grassmannian. With this method we demonstrate exponential alignment for a large (and sharp) class of initial velocity configurations confined to a sector of opening less than $π$. In the case when characteristic parameters remain frozen, the system governs dynamics of opinions for a set of players with constant convictions. Viewed as a dynamical non-cooperative game, the system is shown to possess a unique stable Nash equilibrium, which represents a settlement of opinions most agreeable to all agents. Such an agreement is furthermore shown to be a global attractor for any set of initial opinions.
