Dipal Shah, Sebastian Springer, Heikki Haario, Bernardo Barbiellini, Leonid Kalachev

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1 Scopus citations


Several types of synchronization have been described theoretically and observed experimentally. However, the boundaries between the synchronization states are often blurred. Observing subtle details between different degrees of synchronization is a challenging task not discussed systematically in the literature so far. We present a unified approach that is able to quantify synchronization of chaotic systems by accurately identifying the coupling strength by available measured data. Here, we apply an estimation approach based on summary statistics that are sensitive with respect to changes in the measured time series as well as to the underlying geometry of the attractor of the synchronized system. This method allows distinguishing specific types of synchronizations and monitoring degrees of synchronization in a continuous way, for any values of the coupling strength parameter. As a result, one can identify and quantify both well-known and less discussed, fragile states such as emerging synchronization, chaos suppression, escape events, or unexpected instability occurring at strong couplings strengths.

Original languageEnglish
Pages (from-to)152-176
Number of pages25
JournalFoundations of Data Science
Issue number1
StatePublished - Mar 1 2023


Funding This work was supported by the Centre of Excellence of Inverse Modelling and Imaging (CoE), Academy of Finland, decision numbers 312 122 and 312 125. SS was supported by the Academy of Finland, project number 334 817.

FundersFunder number
Academy of Finland312 125, 334 817, 312 122


    • Chaos suppression
    • Synchronization
    • correlation integral likelihood
    • emerging synchronization
    • feature vector
    • parameter estimation
    • quasi-complete synchronization


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