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Analyzing synchronized nonlinear oscillators is one of the most important andattractive topics in nonlinear science. By understanding the interactionsbetween the oscillators, we can figure out the synchronization process. Apromising approach to the analysis of interacting oscillators in nonlinearscience is the application of the phase model. In this paper, we propose adata-driven approach to extract mutual interactions of synchronized oscillatorsbased on the phase model. Recently, applying machine learning techniques toestimate models in physics has been actively investigated. We propose anoperator-theoretic approach to estimate the phase model of interactingoscillators. We reduce the estimation problem to a multiparameter eigenvalueproblem of the Koopman operator, a linear operator that describes a dynamicalsystem. By reducing the problem to a linear algebraic problem, we cantheoretically show that the proposed approach is stable with respect toperturbations in the given data.

Operator-theoretic Analysis of Mutual Interactions in Synchronized Dynamics