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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. Highlights • Cooperativity metrics in complex systems are affected by both cross- and autocorrelations. • Time delay stability is unaffected by additive while affected by multiplicative white noise. • Coherence is invariant to short-term, while cross-conditional entropy to long-term correlations. • Combination of several metrics provide a better characterization of phase transitions. • Phase transition in geomagnetic network reveals a characteristic pattern during a solar flare. [ABSTRACT FROM AUTHOR]