复发模式的相关性
Gabriel Marghoti1,2, Matheus Palmero Silva2,3, Thiago de Lima Prado1
1Federal University of Paraná, Physics Department, Curitiba, Paraná 81530-015, Brazil.
Physical review. E
|February 20, 2026
概括
我们开发了复杂时间序列数据分析的新方法 - - 重复性模式相关性 (RPC). 与传统的复制图 (RP) 相比,RPC提供了一种更灵活的方法来研究动态系统中的局部结构.
科学领域:
- 非线性动力学是一种非线性动力学.
- 复杂系统分析 复杂系统分析
- 时间序列分析分析时间序列分析
背景情况:
- 重复图 (RPs) 对于可视化时间序列动态非常有价值.
- 传统的复发量化分析通常使用全球指标,缺少局部结构.
- 在定性RP检查和定量分析之间存在差距.
研究的目的:
- 引入复发模式相关性 (RPC) 来弥合复发分析中的差距.
- 开发一种灵活的工具,用于分析反复发生的动态系统中的模式形成.
- 测量RP与任意形状和规模的模式的相关度.
主要方法:
- 引入重复性模式相关性 (RPC),灵感来自空间统计.
- 在物流地图中应用RPC可视化不稳定的分流体.
- 使用RPC剖析标准图的混合相空间.
- 在洛伦兹'63系统中追踪不稳定的周期轨道.
主要成果:
- RPC成功地可视化了传统方法错过的局部结构.
- 该方法揭示了复发模式和潜在的动态特性之间的相关性.
- 在分析各种非线性系统时,RPC表现出灵活性.
结论:
- 复发模式相关性 (RPC) 为时间序列数据提供了更细致的定量分析.
- 复发模式中的长距离相关性编码了关于非线性动态的关键信息.
- RPC提供了一个灵活的框架,用于研究复杂系统中的模式形成.
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