Koopman Analysis And Application Of Chaotic System

Most systems in reality are often difficult to approximate with accurate dy-namical equations due to their complexity,and experimental observations can be used solely to obtain system characteristic data.We hope to find a universal data analysis method to extract key dynamics features underlying a nonlinear system through the characteristic data.The Koopman operator provides an ef-fective mathematical tool,which acts on certain functions and describes their evolution.Based on the time series of the system 's evolution,we can use the Koopman operator to analyze the temporal characteristics of the system,and extract key dynamical factors,and predict the long-term behavior of the system to certain extent.We apply the Koopman operator technique to spectral decom-position of several typical chaotic systems(e.g.Logistic map,Henon map and Lorenz system),effectively extract their key features,and explain the eigenval-ues and eigenfunctions of the Koopman operator.Because of the universality of the analysis,we may apply it to general complex systems.