title: Mutual information rate and bounds for it.
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.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, Scottish Universities Physics Alliance, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: Murilo S
authors.initials: MS
authors.lastname: Baptista
authors.forename: Rero M
authors.initials: RM
authors.lastname: Rubinger
authors.forename: Emilson R
authors.initials: ER
authors.lastname: Viana
authors.forename: José C
authors.initials: JC
authors.lastname: Sartorelli
authors.forename: Ulrich
authors.initials: U
authors.lastname: Parlitz
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007257:Information Theory; D008954:Models, Biological; D013269:Stochastic Processes