Correlation integral

In chaos theory, the correlation integral is the mean probability that the states at two different times are close:

where $N$ is the number of considered states $\vec{x}(i)$ , $\varepsilon$ is a threshold distance, $|| \cdot ||$ a norm (e.g. Euclidean norm) and $\Theta( \cdot )$ the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem):

单词	Correlation integral
释义	Correlation integral 英语百科 Correlation integral In chaos theory, the correlation integral is the mean probability that the states at two different times are close: where $N$ is the number of considered states $\vec{x}(i)$ , $\varepsilon$ is a threshold distance, $\|\| \cdot \|\|$ a norm (e.g. Euclidean norm) and $\Theta( \cdot )$ the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem):
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