Mutual Information Rate and Bounds for It

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.

Northern Research Partnership

Alexander von Humboldt foundation

Engineering and Physical Sciences Research Council grant

Engineering and Physical Sciences Research Council grant [EP/I032606/1]

European Community? Seventh Framework Programme FP7

European Community? Seventh Framework Programme FP7 [HEALTH-F2-2009-241526]

Bernstein Center for Computational Neuroscience II G"ottingen (BCCN grant) [01GQ1005A]

Bernstein Center for Computational Neuroscience II Gottingen (BCCN grant)