耦合群振子的可解范式
A solvable normal form for coupled swarmalators
浏览论文内容
中文总结 AI 辅助
研究群振子模型，基于Tanaka对趋化振荡器的约化，恢复一维群振子模型，推导其集体状态稳定性边界，修正序参公式，揭示非单调同步响应，解决了现有群振子模型缺乏范式基础及相关稳定性等问题。
中文摘要 AI 辅助
群振子是相位振荡器的移动推广，用于模拟同步和自组装相互作用的系统，理论上仍知之甚少。与耦合振荡器的Kuramoto模型不同，现有群振子模型缺乏范式基础，其基本稳定性和分岔问题大多未解决。本文基于Tanaka对趋化振荡器的约化，表明在一次谐波、零滞后极限下可恢复一维群振子模型，推导其四个集体状态的稳定性边界，修正序参公式，揭示Kuramoto模型中不存在的非单调同步响应。
英文摘要
Swarmalators are mobile generalizations of phase oscillators. Introduced to model systems in which sync and self-assembly interact, they remain poorly understood theoretically. Unlike the Kuramoto model for coupled oscillators, existing swarmalator models lack a normal-form foundation, and their basic stabilities and bifurcations remain largely unsolved. Here we address both problems. Building on Tanaka's reduction of chemotactic oscillators, we show that the canonical one-dimensional swarmalator model -- previously introduced as an ad hoc toy model -- is recovered in the first-harmonic, zero-lag limit, implying its behavior is generic. We then derive the stability boundaries organizing its four collective states, show they meet at a single cusp, correct a previously published order-parameter formula, and uncover a non-monotonic sync response absent in the Kuramoto model.
发表机构
- Starling Research Institute（Starling 研究所）
机构由 AI 辅助整理，请以论文原文为准。
