Institute for Complex Systems and Mathematical Biology, Scottish Universities Physics Alliance, University of Aberdeen, Aberdeen, United Kingdom.
PLoS One. 2012;7(10):e46745. doi: 10.1371/journal.pone.0046745. Epub 2012 Oct 24.
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.
在动态网络中两个节点之间或两个数据集之间，单位时间内交换的信息量是分析复杂系统的一个有力概念。这个量被称为互信息率（MIR），是从互信息中计算出来的，互信息仅在随机系统中被严格定义。此外，互信息的定义是基于重大事件的概率。这项工作提供了一种简单的方法来计算动态（确定性）网络或两个时间序列（不完全确定性）之间的 MIR，并计算其上下界，而无需计算概率，而是根据动态系统中已知和定义良好的量来计算。作为我们界限的可能应用，我们研究了两个耦合映射系统和实验耦合振荡器网络中的同步和信息交换之间的关系。
