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.
Publication types
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Research Support, Non-U.S. Gov't
MeSH terms
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Algorithms
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Computer Simulation
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Information Theory*
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Models, Biological
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Stochastic Processes
Grants and funding
MSB was partially supported by the Northern Research Partnership, Alexander von Humboldt foundation, and the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. The research leading to the results has received funding from the European Community? Seventh Framework Programme FP7/2007-2013 under grant agreement No. HEALTH-F2-2009-241526, EUTrigTreat. Furthermore, support by the Bernstein Center for Computational Neuroscience II G\"ottingen (BCCN grant 01GQ1005A, project D1) is acknowledged. RR, EV and JCS thanks the Brazilian agencies Coordenadoria de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do estado de Minas Gerais and Fundação de Amparo à Pesquisa do Estado de São Paulo. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.