用递归网络量化混沌吸引子的信息损失
Quantifying information loss on chaotic attractors through recurrence networks
摘要：
我们提出了一个熵测度的混沌吸引子的分析通过递归网络，这是无权和无向的复杂网络构造的时间序列的动力系统，使用特定的标准。我们表明，建议的措施收敛到一个常数的吸引子（或网络上的节点数）和嵌入维数的增加用于网络的建设的数据点的数量，并清楚地区分递归网络从混沌时间序列和白噪声。由于该措施是网络拓扑结构的特点，它可以用来量化的信息损失与混沌吸引子的结构变化的差异在相应的递归网络的链接密度。我们还指出了一些实际应用中提出的措施，在混沌吸引子的递归分析以及相关的复杂网络的一般理论的背景下，提出的措施。
英文摘要：
We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that the proposed measure converges to a constant value with increase in the number of data points on the attractor (or the number of nodes on the network) and the embedding dimension used for the construction of the network, and clearly distinguishes between the recurrence network from chaotic time series and white noise. Since the measure is characteristic to the network topology, it can be used to quantify the information loss associated with the structural change of a chaotic attractor in terms of the difference in the link density of the corresponding recurrence networks. We also indicate some practical applications of the proposed measure in the recurrence analysis of chaotic attractors as well as the relevance of the proposed measure in the context of the general theory of complex networks.
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