如何通过更高阶网络结构增强自适应同步能力?
Qiuyue Zhao1,2, Lilan Tu1,2, Jia Hu1,2
1Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China.
Chaos (Woodbury, N.Y.)
|February 19, 2026
概括
降低控制成本和提高高阶网络中的同步性至关重要. 较小的网络尺寸和合强度降低了成本,而增加2个简单则改善了自适应同步,特别是在Erdős-Rényi简单化的复杂网络中.
科学领域:
- 复杂的网络 复杂的网络
- 网络同步 网络同步
- 控制理论 控制理论
背景情况:
- 高阶动态网络,包括一阶 (边缘) 和二阶 (2 简单) 交互,存在复杂的同步挑战.
- 降低控制成本和提高同步能力是网络科学和工程中的关键问题.
研究的目的:
- 在使用利亚普诺夫稳定理论的更高阶动态网络中推导适应同步的足够条件.
- 调查网络结构和参数对控制成本和同步性能的影响.
- 为了比较不同高级网络模型的自适应同步能力和稳定性.
主要方法:
- 基于利亚普诺夫稳定理论的理论框架的开发,以确保自适应同步.
- 三种不同的高阶网络模型的构建和分析:埃尔多斯-雷尼简化复合 (ERSC),瓦茨-斯特罗格茨简化复合 (WSSC) 和巴巴西-阿尔伯特简化复合 (BASC).
- 在这些网络模型中分析一级和二级度分布.
- 通过数值模拟进行验证,以评估理论发现.
主要成果:
- 较小的网络规模和合强度有效地降低了所有研究的网络类型的控制成本和能源消耗.
- 埃尔多斯-雷尼简单复合 (ERSC) 网络表现出卓越的自适应同步能力,增加了2-simplices的数量.
- 与ERSC和巴拉巴西-阿尔伯特简化复合 (BASC) 网络相比,Watt-Strogatz简化复合 (WSSC) 网络在变化合强度或2个简单的数量时表现出更大的稳定性.
结论:
- 该研究为高阶网络中的自适应同步提供了理论条件,为成本降低和性能提升提供了洞察力.
- 网络拓和参数选择显著影响同步效率和控制成本,ESRC和WSSC显示出明显的优势.
- 研究结果表明,优化网络结构,特别是更高阶简单数和合强度的优化,是实现高效和强大的自适应同步的关键.
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