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This paper proposes an original methodology to compute the regions ofattraction in hyperbolic and polynomial nonlinear dynamical systems using theeigenfunctions of the discrete-time approximation of the Koopman operator givenby the extended dynamic mode decomposition algorithm. The proposed methodrelies on the spectral decomposition of the Koopman operator to buildeigenfunctions that capture the boundary of the region of attraction. Thealgorithm relies solely on data that can be collected in experimental studiesand does not require a mathematical model of the system. Two examples ofdynamical systems, a population model and a higher dimensional chemicalreaction system, allows demonstrating the reliability of the results.

Evaluation of the Region of Attractions of Higher Dimensional Hyperbolic Systems using the Extended Dynamic Mode Decomposition