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原文連結
論文資訊
- 類型：已發表論文
- 日期：2012
摘要
Recurrence 網絡s are a novel tool of 非線性 time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this letter, we demonstrate that recurrence 網絡s obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with 縮放律 exponents gamma that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that gamma is not related to the 碎形 dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent gamma depending on a suitable notion of local dimension, and such with fixed gamma=1.
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