库拉莫托模型在复杂网络上的丧同步
Géza Ódor1, Shengfeng Deng2, Jeffrey Kelling3,4
1Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary.
Entropy (Basel, Switzerland)
|January 8, 2025
概括
我们在大型网络上研究了Kuramoto模型中的同步过渡. 网络异质性导致挫败的同步,不同于常规格子.
科学领域:
- 复杂的系统复杂的系统.
- 网络科学 网络科学
- 统计物理学的统计物理.
背景情况:
- 库拉莫托模型是研究合振荡器系统同步现象的标准框架.
- 了解大型和复杂网络中的同步过渡对于各种科学领域至关重要.
- 与常规网格相比,具有远程连接的异质网络可以表现出不同的动态行为.
研究的目的:
- 调查局部合的库拉莫托模型在极大规则格子和异质网络上的同步过渡,具有权力规律衰变的长链接.
- 为了比较这些不同的网络结构中同步的关键行为和扩展特性.
- 阐明网络异质性在同步动态中的作用.
主要方法:
- 在大型正则格子 (405x405和1004x1004) 和异质网络 (12,000x12,000) 上使用库拉莫托模型的模拟,具有权力规律衰变的长链接.
- 使用光谱维度 (ds) 和调整缩放的概念对同步过渡的分析.
- 平均场和非平均场关键行为的比较.
主要成果:
- 正则格子显示平均场的临界性,在d=4时进行对数校正,在d=5时进行强度校正.
- 带有长链的异质网络表现出非平均场涂抹过渡,在高光谱维度 (ds>4) 上有振荡校正.
- 网络异质性显著改变了同步动态,导致了失败的同步.
结论:
- 具有长链路的网络的异质性是影响同步过渡的关键因素.
- 在异质网络中观察到的挫败同步类似于格里菲斯效应.
- 这项研究强调了网络拓在确定集体动态和相位转换方面的重要性.
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