具有标签交换的多智能体系统的Boltzmann型方程
Boltzmann-type equations for multi-agent systems with label switching
摘要：
在本文中，我们提出了一个玻尔兹曼型动力学描述的质量变化的相互作用的多智能体系统。我们的代理人的特征是微观状态，由于它们的相互作用而发生变化，并且通过标签来识别它们所属的组。除了组内和组间的交互外，智能体还可以根据状态依赖的马尔可夫型跳转过程来改变标签。我们推导出一般的动力学方程的联合相互作用/标签开关过程中的每一组。对于典型的出生/死亡动力学，我们通过福克-普朗克渐近分析，通过瞬态和平衡动力学分布的群体。然后，我们介绍和分析了一个简单的模型的传染病的传染，利用联合互动/标签开关过程来描述检疫措施。
英文摘要：
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
