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Entropy 2013, 15(8), 3186-3204;

Linearized Transfer Entropy for Continuous Second Order Systems

Naval Research Laboratory, Optical Sciences Division, Washington DC 20375, USA
Naval Research Laboratory, Optical Science Division, Washington DC 20375, USA
Permanent Address: Global Strategies Group, Crofton, MD 21114, USA
Author to whom correspondence should be addressed.
Received: 22 May 2013 / Revised: 5 July 2013 / Accepted: 18 July 2013 / Published: 7 August 2013
(This article belongs to the Special Issue Transfer Entropy)
PDF [397 KB, uploaded 24 February 2015]


The transfer entropy has proven a useful measure of coupling among components of a dynamical system. This measure effectively captures the influence of one system component on the transition probabilities (dynamics) of another. The original motivation for the measure was to quantify such relationships among signals collected from a nonlinear system. However, we have found the transfer entropy to also be a useful concept in describing linear coupling among system components. In this work we derive the analytical transfer entropy for the response of coupled, second order linear systems driven with a Gaussian random process. The resulting expression is a function of the auto- and cross-correlation functions associated with the system response for different degrees-of-freedom. We show clearly that the interpretation of the transfer entropy as a measure of "information flow" is not always valid. In fact, in certain instances the "flow" can appear to switch directions simply by altering the degree of linear coupling. A safer way to view the transfer entropy is as a measure of the ability of a given system component to predict the dynamics of another.
Keywords: transfer entropy; joint entropy; coupling transfer entropy; joint entropy; coupling
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Nichols, J.M.; Bucholtz, F.; Michalowicz, J.V. Linearized Transfer Entropy for Continuous Second Order Systems. Entropy 2013, 15, 3186-3204.

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