在复杂系统的关键转换过程中出现反复凝结
Manaswini Jella1,2, Induja Pavithran2,3, Vishnu R Unni4
1Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos (Woodbury, N.Y.)
|August 1, 2025
概括
这项研究引入了反复性分析,以检测复杂系统中的关键过渡,如流体. 该方法被称为"反复凝聚",可以识别从混乱到周期性行为的转变,即使在杂的数据中也是如此.
科学领域:
- 复杂系统动力学 复杂系统动力学
- 流体力学 流体力学 流体力学
- 非线性动力学是一种非线性动力学.
背景情况:
- 复杂系统中的关键过渡可以导致自然和工程系统的灾难性故障.
- 检测这些关键点是具有挑战性的,特别是在杂的,高维的系统.
- 流体系统表现出复杂的动态,难以预测和控制临界点附近.
研究的目的:
- 在流体系统中,利用复发性分析,研究从混乱振荡到周期性振荡的关键过渡.
- 开发一种方法来检测噪音系统中的关键点,并进行逐步过渡.
- 命名和量化观察到的"反复凝结"现象.
主要方法:
- 在来自流体系统的时间序列数据上使用了复杂度图 (RP) 和复杂度量化措施 (RQM).
- 分析了从无序结构到有序结构的复发模式的演变.
- 使用诸如复发时间,确定性,,层次性和捕获时间等指标量化的"复发凝结".
主要成果:
- 复杂性图表显示出明显的进展,表明从多个时间尺度向主导的单个时间尺度 ("复杂性凝结") 的转变.
- 复发量化指标崩到一个单一的主导时间尺度,证实了过渡.
- 复杂性测量显示了权力法在临界点附近的缩放,允许精确检测临界参数值.
结论:
- 反复分析,特别是"反复凝结",是检测杂,复杂系统中的关键转换的有效方法.
- 该方法成功地确定了合成杂的Hopf分叉模型中的关键点,与分叉点一致.
- 这种方法为识别各种科学和工程领域定义不良的过渡点提供了有价值的见解.
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