Assessment of cooperativity in complex systems with non-periodical dynamics: Comparison of five mutual information metrics

Abstract

Quantitative assessment of cooperativity effects is essential for a better understanding of the interactions between system components that is an important step on the way from black-box to structural models of various complex dynamical systems. In this paper, we consider five widely used mutual information metrics and test their performance using simulated stochastic data series with introduced phase- or amplitude randomization as well as data series generated by chaotic maps. We show the performance of all studied methods in both stationary mode and during phase transitions, indicating specific coupling patterns they can reveal from the system dynamics, as well as certain properties they appear invariant to. Finally, we demonstrate how a combination of several metrics can be used for a more detailed analysis of dynamical systems exhibiting characteristic phase transitions, including examples of both simulated chaotic maps and observational data series from physiological and geophysical complex systems.