Tracking bifurcation curves in the Hénon map from only time-series datasets
Tracking bifurcation curves in the Hénon map from only time-series datasets
复制标题
仅从时间序列数据集跟踪 Hénon 图中的分岔曲线
DOI：
10.1587/nolta.10.268
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Adachi
中科院分区：
文献类型：
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作者：
Y. Itoh;M. Adachi
我们描述了一种方法，用于跟踪分歧曲线，从时间序列数据集。我们应用跟踪算法的基础上重建的分岔图，可以估计参数空间和振荡模式时，参数变化的未知系统。因此，该方法可以跟踪未知系统的分岔曲线，而以前的研究中的目标系统是已知的，只有测量的时间序列数据集。通过跟踪分叉曲线，我们可以得到更高精度的分叉点，与用蛮力法绘制的分叉图相比。在本文中，我们提出的数值实验中，Hénon映射作为一个未知系统的分支曲线跟踪只有几个时间序列数据集的结果。
We describe a method for tracking bifurcation curves from only time-series datasets. We apply a tracking algorithm to unknown systems based on the reconstruction of bifurcation diagrams that can estimate the parameter space and oscillatory patterns when parameters change. Therefore, this method can track the bifurcation curves of unknown systems from only measured time-series datasets, whereas the target systems in previous studies are known. By tracking bifurcation curves, we can obtain bifurcation points with increased accuracy as compared with bifurcation diagrams plotted by brute-force methods. In this paper, we present the results of numerical experiments in which bifurcation curves of a Hénon map as an unknown system are tracked from only several time-series datasets.