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研究生:黃冠穎
研究生(外文):Huang, Guan-Ying
論文名稱:在一類具有特殊本質加速度的兩生物體 Cucker-Smale 模 型中的群聚現象
論文名稱(外文):Flocking in a Two-Agent Cucker-Smale Model with Some Special Intrinsic Accelerations
指導教授:梁育豪
指導教授(外文):Liang, Yu-Hao
口試委員:莊重謝世峰
口試委員(外文):ZHUANG, ZHONGXIE, SHI-FENG
口試日期:2021-08-26
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:應用數學系碩博士班
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:32
中文關鍵詞:Cucker-Smale 模型本質加速度群聚
外文關鍵詞:Cucker-Smale modelsintrinsic accelerationsflocking
相關次數:
  • 被引用被引用:0
  • 點閱點閱:66
  • 評分評分:
  • 下載下載:1
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文中,我們考慮了兩生物體的增強Cucker-Smale 模型,其中生物體的本質加
速度由兩個不同的函數控制。在文獻中,已經對具有本質加速度的增強Cucker-Smale 模
型進行了充分研究。然而,所有工作都假設模型中所有生物體的本質加速度受相同函數的
支配。在這項工作中,我們的目標是通過考慮一個特殊的模型來放寬這個限制。在模型中
群聚的充分條件是從理論上推導出來的。此外,還提供了數值模擬來支持我們的理論結
果。
In this paper, we consider an augmented Cucker-Smale model of two agents, where intrinsic
accelerations of agents are governed by two different functions. In literature, augmented
Cucker-Smale models with intrinsic accelerations have been well-studied. However, all of
these works assumed that intrinsic accelerations of all agents in models are governed by the
same function. In this work, we aim at relaxing this restriction by considering a special
model. The sufficient conditions for flocking in our model are derived theoretically. As well,
numerical simulations to support our theoretical results are provided.
Contents
1 Introduction 5
2 A Simplified Model of (1.5): Constant Coupling Strength 8
3 A Simplified Model of (1.5): Time-Varying Coupling Strength 16
4 Conditions for Flocking in Model (1.5) 22
5 Conclusion 28
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