复杂系统中的顺序参数动态:从模型到数据
Zhigang Zheng1, Can Xu1, Jingfang Fan2
1Institute of Systems Science, Huaqiao University, Xiamen 361021, China and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Chaos (Woodbury, N.Y.)
|February 11, 2024
概括
本综述探讨了使用顺序参数动态的复杂系统中的集体动态. 它引入了自微状态方法 (EMP) 来分析难以建模的系统,揭示新兴的集体行为.
科学领域:
- 复杂系统科学 复杂系统科学
- 统计物理 统计物理
- 非线性动力学是一种非线性动力学.
背景情况:
- 集体订单行为在复杂的系统中很常见,来自自我组织和合.
- 顺序参数量化了从多个自由度中出现的过渡到集体状态.
- 协同效应学为理解自我组织和集体动态提供了一个框架.
研究的目的:
- 通过顺序-参数动态的镜头来审查复杂系统的集体动态.
- 介绍在基于模型和基于数据的场景中构建订单参数动态的方法.
- 引入自身微态方法 (EMP) 用于分析具有挑战性建模的复杂系统.
主要方法:
- 协同理论和奴役原则,从慢模式定义订单参数.
- 基于模型的系统的分析缩小程序 (例如,奥特-安东森,洛伦茨套用)
- 自微态方法 (EMP) 通过自态分解从大数据中重建顺序参数动态.
主要成果:
- 顺序参数动力学成功地描述了同步,嵌合体状态和神经元网络动力学.
- EMP有效地捕捉了宏观的集体行为,包括波斯-爱因斯坦凝聚式的过渡和主导特征模式的出现.
- EMP应用在阶段过渡 (Ising模型),气候动态,股票市场波动和生物系统的集体运动方面取得了成功.
结论:
- 顺序参数动态为理解复杂系统中的集体行为提供了一个强大的框架.
- 固有微态方法 (EMP) 为分析复杂系统提供了一种新的数据驱动方法.
- 这种方法将不同科学领域的集体现象研究统一起来.
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