A mean-field approach for the asymptotic tracking of continuum target clouds
主講人：Seung Yeal Ha
Seung-Yeal Ha 教授，韓國科學與工程院院士、首爾國立大學數學系教授，韓國科學獎、青年科學獎、KSIAM-Kumkok獎的獲得者，國際數學家大會45分鐘報告人。主要研究方向為雙曲守恒律，氣體動力學理論，多智能體系統的群體行為。
内容摘要：
In this talk, we propose a new coupled kinetic system arising from the asymptotic tracking of a continuum target cloud, and study its asymptotic tracking property. For the proposed kinetic system, we present an energy functional which is monotonic and distance between particle trajectories corresponding to kinetic equations for target, and tracking ensembles tend to zero asymptotically under a suitable sufficient framework. The framework is formulated in terms of system parameters and initial data. This is a joint work with Hyunjin Ahn (Myongji Univ. Korea)
Kinetic modeling of a leader-follower system in crowd evacuation with collective learning
主講人：廖傑
廖傑，上海财經大學數學學院教授、博士生導師。研究方向：多智能體系統建模和數學理論分析。在Mathematical Models and Methods in Applied Sciences 、Proceedings of the Royal Society of Edinburgh, Section A: Mathematics、Journal of Statistical Physics、 Journal of Differential Equations 等國際重要期刊上發表學術論文20餘篇。
内容摘要：
The kinetic modeling approach can be applied effectively to model collective behavior of human crowds. We present a kinetic modeling on crowd evacuation of a system with leaders and followers, as well as their collective learning. Numerical comparison of evacuation with and without learning shows a reasonably good predictive ability of the model that the learning effect plays a significant role in the evacuation dynamics.
On a generalized Kuramoto-type model and voting dynamics
主講人：李祝春
李祝春，哈爾濱工業大學教授、博士生導師，研究方向: 集群動力學、群體智能及應用. 在SIAM Journal on Applied Dynamical Systems、 SIAM Journal on Control and Optimization、 Nonlinearity、Mathematical Models and Methods in Applied Sciences等國際重要期刊上發表學術論文30餘篇。
内容摘要：
In this talk, we discuss a variant of Kuramoto model which possess some nice properties which extend to voting dynamics. In this model, phases are forced to approach bipolar states, thereby stabilizing them. This induces multi-stability and results in complex asymptotic behaviors. This system can be extended to model the voting dynamics on a binary electoral question and describe the formation of voting decision in a community.