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arXiv 1502.03527nlin.CD
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混沌时间序列递归网络分析的统一框架

Uniform framework for the recurrence-network analysis of chaotic time series

Rinku Jacob, K. P. Harikrishnan, R. Misra, G. Ambika

备注：
26 pages, 18 figures
发表信息：
Physical Review E 93, 012202 (2016)
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摘要：

提出了一种从混沌时间序列构造和分析无权$ε$ -递归网络的一般方法。在我们的方案中的临界阈值$ε_c$的选择是经验性的，我们表明，它的值是密切相关的嵌入维数$M$。事实上，我们能够确定一个小的临界范围$Δε$数字是近似相同的随机和几个标准的混沌时间序列为一个固定的$M$。这为我们提供了一个统一的框架，非主观比较的统计措施的递归网络构造的各种混沌吸引子。我们明确地表明，我们的计划所构建的递归网络的度分布的吸引子的结构和显示统计尺度不变性相对于增加的节点数$N$。我们还提出了两个实际应用的计划，检测两个动力学制度之间的过渡时间延迟系统和识别的基础系统的维数从现实世界的数据与有限的点，通过递归网络措施。文中还讨论了该方法的优点、局限性和应用前景。

英文摘要：

We propose a general method for the construction and analysis of unweighted $ε$ - recurrence networks from chaotic time series. The selection of the critical threshold $ε_c$ in our scheme is done empirically and we show that its value is closely linked to the embedding dimension $M$. In fact, we are able to identify a small critical range $Δε$ numerically that is approximately the same for the random and several standard chaotic time series for a fixed $M$. This provides us a uniform framework for the non subjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors. We explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes $N$. We also present two practical applications of the scheme, detection of transition between two dynamical regimes in a time delayed system and identification of the dimensionality of the underlying system from real world data with limited number of points, through recurrence network measures. The merits, limitations and the potential applications of the proposed method have also been highlighted.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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