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通过在离散动态系统中的时间序列数据集和参数上训练的极端学习机器方法来预测分叉点
Kaito Kato1, Yoshitaka Itoh2, Takuji Kousaka1
1Chukyo University, 101-2 Yagoto Honmachi, Showa-ku, Nagoya, Aichi 466-8666, Japan.
Physical review. E
|August 19, 2025
概括
本研究介绍了一种数据驱动的极端学习机器与输入参数通道 (ELM-IPC) 方法,以准确地找到离散动态系统中的分叉点. 该方法有效地分析复杂的系统,即使存在并存或长期周期性的解决方案.
科学领域:
- 动态系统和混沌理论
- 计算智能是一种计算智能.
- 非线性动力学是一种非线性动力学.
背景情况:
- 分叉点对于理解系统行为至关重要.
- 传统方法与复杂的系统和长期周期性解决方案作斗争.
- 准确识别分叉点对于系统分析至关重要.
研究的目的:
- 提出一种新的数据驱动方法来识别分叉点.
- 增强使用输入参数通道 (ELM-IPC) 的极端学习机器对离散动态系统的分析.
- 证明该方法在复杂系统上的有效性.
主要方法:
- 使用在时间序列数据上训练的输入参数通道 (ELM-IPC) 的极端学习机器.
- 通过输入参数通道将原始参数空间与ELM-IPC衍生的参数空间对齐.
- 将该方法应用于Hénon地图和合的Hénon地图系统.
主要成果:
- ELM-IPC方法准确地识别了离散动态系统中的分叉点.
- 该方法成功地处理参数空间与共存的解决方案.
- 有效地检测系统中的分叉点,周期溶液超过100的周期.
结论:
- 拟议的ELM-IPC方法为分叉点分析提供了强大的数据驱动方法.
- 这种技术促进了复杂的离散动态系统的研究.
- 能够在具有挑战性的参数模式中准确地描述系统动态.
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