Directed Flow of Information in Chimera States

We investigated interactions within chimera states in a phase oscillator networkwith two coupled subpopulations. To quantify interactions within and between thesesubpopulations, we estimated the corresponding (delayed) mutual information that—ingeneral—quantifies the capacity or the maximum rate at which information canbe transferred to recover a sender’s information at the receiver with a vanishinglylow error probability. After verifying their equivalence with estimates based on thecontinuous phase data, we determined the mutual information using the time pointsat which the individual phases passed through their respective Poincaré sections. Thisstroboscopic view on the dynamics may resemble, e.g., neural spike times, that arecommon observables in the study of neuronal information transfer. This discretizationalso increased processing speed significantly, rendering it particularly suitable for afine-grained analysis of the effects of experimental and model parameters. In ourmodel, the delayed mutual information within each subpopulation peaked at zerodelay, whereas between the subpopulations it was always maximal at non-zero delay,irrespective of parameter choices. We observed that the delayed mutual informationof the desynchronized subpopulation preceded the synchronized subpopulation. Putdifferently, the oscillators of the desynchronized subpopulation were “driving” the onesin the synchronized subpopulation. These findings were also observed when estimatingmutual information of the full phase trajectories. We can thus conclude that the delayedmutual information of discrete time points allows for inferring a functional directed flowof information between subpopulations of coupled phase oscillators.