  We investigated interactions within chimera states in a phase oscillator
network with two coupled subpopulations. To quantify interactions within and
between these subpopulations, we estimated the corresponding (delayed) mutual
information that -- in general -- quantifies the capacity or the maximum rate
at which information can be transferred to recover a sender's information at
the receiver with a vanishingly low error probability. After verifying their
equivalence with estimates based on the continuous phase data, we determined
the mutual information using the time points at which the individual phases
passed through their respective Poincar\'{e} sections. This stroboscopic view
on the dynamics may resemble, e.g., neural spike times, that are common
observables in the study of neuronal information transfer. This discretization
also increased processing speed significantly, rendering it particularly
suitable for a fine-grained analysis of the effects of experimental and model
parameters. In our model, the delayed mutual information within each
subpopulation peaked at zero delay, whereas between the subpopulations it was
always maximal at non-zero delay, irrespective of parameter choices. We
observed that the delayed mutual information of the desynchronized
subpopulation preceded the synchronized subpopulation. Put differently, the
oscillators of the desynchronized subpopulation were 'driving' the ones in the
synchronized subpopulation. These findings were also observed when estimating
mutual information of the full phase trajectories. We can thus conclude that
the delayed mutual information of discrete time points allows for inferring a
functional directed flow of information between subpopulations of coupled phase
oscillators.
