在有动态噪声的情况下进行通用同步,并通过循环神经网络检测其
José M Amigó1, Roberto Dale1, Juan C King1
1Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain.
Chaos (Woodbury, N.Y.)
|December 17, 2024
概括
本研究介绍了一种方法来检测合的非线性系统中的通用同步,即使有噪音数据. 该方法扩展了现有的技术,在复杂的时间序列分析中识别功能依赖.
科学领域:
- 非线性动力学是一种非线性动力学.
- 时间序列分析时间序列分析.
- 复杂的系统复杂的系统.
背景情况:
- 一般化同步发生在一个系统 (响应器) 接着另一个系统 (驱动器) 时.
- 这种同步是数学描述的同步地图.
- 交叉地图对于检测功能依赖至关重要,它在重建的状态空间中将驱动器和响应器状态联系起来.
研究的目的:
- 在驱动系统中存在噪声时,研究通用同步.
- 将同步和交叉映射的概念扩展到杂的场景中.
- 开发和验证一种在现实的噪音条件下检测通用同步的方法.
主要方法:
- 使用一个带有参数的驾驶动态家族来建模噪音.
- 将同步和交叉映射扩展到取决于噪声参数的家庭.
- 利用循环神经网络和可预测性来检测更高周期同步图.
主要成果:
- 同步和交叉映射可以概括到杂的场景.
- 拟议的方法成功地在无噪声和噪声条件下识别了通用同步.
- 验证使用合成和现实世界的时间序列数据进行.
结论:
- 开发的方法有效地检测到在存在驾驶员噪音的情况下的通用同步.
- 这项工作为分析现实噪音水平的复杂系统中的功能依赖提供了强大的框架.
- 使用更高周期同步图和神经网络为非线性时间序列分析提供了强大的工具.
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