在计算相关性维度和最大Liapunov指数时,用于识别线性区域的新方法
Shuang Zhou1, Shiyu Wang1, Herbert Ho-Ching Iu2
1School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China.
Chaos (Woodbury, N.Y.)
|December 2, 2025
概括
本研究引入了一种用于识别线性区域的新方法,用于计算相关维度 (D2) 和最大利亚普诺夫指数 (LLE). 该方法使用单一目标编程来准确有效地分析混乱系统.
科学领域:
- 非线性动力学和混沌理论.
- 复杂系统分析.
- 数据科学和计算方法.
背景情况:
- 准确计算相关性维度 (D2) 和最大利亚普诺夫指数 (LLE) 对于描述混乱系统至关重要.
- 在关联积分图中确定正确的线性区域是一个关键但具有挑战性的步骤.
- 现有的方法可能涉及复杂的计算或缺乏稳定性来确定这个关键的间隔.
研究的目的:
- 提出一种新的动态范围识别方法,用于准确确定线性区域.
- 为了提高相关性维度 (D2) 和最大利亚普诺夫指数 (LLE) 的计算.
- 为现有方法提供一个计算效率高和强大的替代方案.
主要方法:
- 使用已确定的算法计算相关积分和平均差异指数的计算 (Grassberger-Procaccia,Rosenstein等. ) 的情况.
- 应用单目标编程理论,最大化间隔长度,同时确保合适的准确性和变量相关性.
- 最小正方形方法适应已识别的线性区域以获得D2和LLE值.
主要成果:
- 拟议的方法成功地识别了最佳的线性区域,并具有很高的准确度.
- 数字模拟证实了该方法在计算D2和LLE时的有效性.
- 结果与主流方法相似,但通过更简单的计算过程实现.
结论:
- 基于单一目标编程的动态范围识别方法为分析混乱系统提供了有效和高效的方法.
- 这种方法简化了线性区域识别的复杂过程,用于计算关键动态不变量.
- 该研究提出了一个新的概念框架,用于确定时间序列分析中的线性间隔.
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