本頁只刊出中文翻譯與中文說明；英文原文請見下方原文連結。
原文連結
論文資訊
- 類型：已發表論文
- 日期：2025
摘要
From the formation of ice in small clusters of water molecules to the mass raids of army ant colonies, the emergent behavior of collectives depends critically on their size. At the same time, common wisdom holds that such behaviors are robust to the loss of individuals. This tension points to the need for a more systematic study of how number influences 集體行為. We initiate this study by focusing on 集體行為s that change abruptly at certain critical numbers of individuals. We show that a subtle modification of standard 分岔 analysis identifies such critical numbers, including those associated with discreteness- and noise-induced transitions. By treating them as instances of the same phenomenon, we show that critical numbers across physical scales and scientific domains commonly arise from competing
※ 此為已發表論文，全文需透過期刊付費取得