Abstract
In Chap. 5 we have discussed how to calculate several variants of information contained within a timeseries or set. But an equally interesting question is how much information is shared between two different timeseries. Answering this allows us to say how much they are “correlated” with each other, which is useful in practical applications. It is also possible to take this a step further and ask about information transfer (i.e., directed information flow) between timeseries, which can become a basis for inferring connections between sub-components of a system. This is used in many different fields, as for example neuroscience. We close the chapter by discussing the method of surrogates, which is used routinely in nonlinear dynamics, e.g., for identifying nonlinearities in measured timeseries.
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Besides the unidirectional local coupling there is also the global coupling “around the circle” that results in a very weak impact of \(x^{(m)}\) on \(x^{(m-1)}\).
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Datseris, G., Parlitz, U. (2022). Information Across Timeseries. In: Nonlinear Dynamics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-91032-7_7
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DOI: https://doi.org/10.1007/978-3-030-91032-7_7
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