Mutual information rate and bounds for it

TL;DR

This paper introduces a new method to calculate the mutual information rate and its bounds in dynamical systems, avoiding probability calculations, with applications to coupled maps and oscillators.

Contribution

It provides a simple approach to estimate MIR and bounds directly from dynamical system properties, extending analysis to deterministic and data-driven networks.

Findings

Derived bounds for MIR in dynamical systems.

Applied bounds to coupled maps and oscillators.

Established relationship between synchronization and information exchange.

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 data sets (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.