engleski

The Application of Koopman Operator-based Algorithms to Nonautonomous and Stochastic Systems

In practice, a complex dynamical system often include some time-dependent or random forcing so that it can not be modeled as autonomous system. Therefore, the extension of the Koopman operator theory to nonautonomous and stochastic systems is of great importance. It brings a new viewpoint to the existing theory of nonautonomous and random dynamical systems, particularly, with application of Koopman operator-based data-driven algorithms. We consider the nonautonomous Koopman operator family based on the skew-product definition of the nonautonomous dynamical system. Similarly, we introduce the stochastic Koopman operator family associated with the given random dynamical system. In both cases, we state basic properties of the operator and discuss the application of Koopman-operator based algorithms on the considered systems. The performance of the algorithms is illustrated in the context of discovering the spectral objects of the system, as well as, on the reconstruction and prediction of the system behaviour.

Koopman operator, DMD algorithm, Vandermonde algorithm, Nonautonomous system, Random dynamical system

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