Research On The Algorithms And Applications Of Koopman Operator On Some Dynamical Systems

Analysis of complex dynamical systems is an important subject in many areas.Nowadays, enormous amount of data is obtained via high-throughput experments or largescale simulations, which leads to various development of many data processing techniques. This article discusses algorithms based on the spectral properties of Koopman operator to deal with discrete time series generated by different dynamical systems. Koopman operator describes evolution of observables. We get its eigenfunctions and Koopman modes by studying its spectrum. On one hand, the eigenfunctions can be used to partition the phase space, reducing massive data to a small amount of characteristic states. On the other hand, the Koopman modes represent interesting dynamical patterns in the evolution of the system, which help us get more insight into the system.