応用解析セミナー
過去の記録 ~12/05|次回の予定|今後の予定 12/06~
開催情報 | 木曜日 16:00~17:30 数理科学研究科棟(駒場) 002号室 |
---|---|
担当者 | 石毛 和弘 |
2024年04月11日(木)
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催
Jan Haskovec 氏 (KAUST, Saudi Arabia)
Non-Markovian models of collective motion (English)
https://forms.gle/5cZ4WzqBjhsXrxgU6
対面・オンラインハイブリッド開催
Jan Haskovec 氏 (KAUST, Saudi Arabia)
Non-Markovian models of collective motion (English)
[ 講演概要 ]
I will give an overview of recent results for models of collective behavior governed by functional differential equations with non-Markovian structure. The talk will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. I will characterize two main sources of delay - inter-agent communications ("transmission delay") and information processing ("reaction delay") - and discuss their impacts on the group dynamics. I will give an overview of analytical methods for studying the asymptotic behavior of the models in question and their mean-field limits. In particular, I will show that the transmission vs. reaction delay leads to fundamentally different mathematical structures and requires appropriate choice of analytical tools. Finally, motivated by situations where finite speed of information propagation is significant, I will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
[ 参考URL ]I will give an overview of recent results for models of collective behavior governed by functional differential equations with non-Markovian structure. The talk will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. I will characterize two main sources of delay - inter-agent communications ("transmission delay") and information processing ("reaction delay") - and discuss their impacts on the group dynamics. I will give an overview of analytical methods for studying the asymptotic behavior of the models in question and their mean-field limits. In particular, I will show that the transmission vs. reaction delay leads to fundamentally different mathematical structures and requires appropriate choice of analytical tools. Finally, motivated by situations where finite speed of information propagation is significant, I will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
https://forms.gle/5cZ4WzqBjhsXrxgU6