Mutual information rate and bounds for it

Murilo S Baptista; Rero M Rubinger; Emilson R Viana; Jose C Sartorelli; Ulrich Parlitz; Celso Grebogi

doi:10.1371/journal.pone.0046745

Mutual information rate and bounds for it

Murilo S Baptista, Rero M Rubinger, Emilson R Viana, Jose C Sartorelli, Ulrich Parlitz, Celso Grebogi

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Abstract

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Original language	English
Article number	e46745
Number of pages	10
Journal	PloS ONE
Volume	7
Issue number	10
DOIs	https://doi.org/10.1371/journal.pone.0046745
Publication status	Published - 24 Oct 2012

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AU - Parlitz, Ulrich

AU - Grebogi, Celso

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AB - The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

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Mutual information rate and bounds for it

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