Directed Flow of Information in Chimera States

Nicolás Deschle*, Andreas Daffertshofer, Demian Battaglia, Erik A. Martens

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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 Poincaré 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.

Original languageEnglish
Article number28
Pages (from-to)1-8
Number of pages8
JournalFrontiers in Applied Mathematics and Statistics
Issue numberJUNE
Publication statusPublished - 25 Jun 2019


ND and AD want to thank to Rok Cestnik and Bastian Pietras for fruitful discussions. Funding. This study received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sk?odowska-Curie grant agreement #642563 (COSMOS).

FundersFunder number
Horizon 2020 Framework Programme
Horizon 2020642563


    • chimera states
    • coupled networks
    • information flow
    • mutual information
    • phase oscillators


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