Correlation dimensional analytical instrument and Lyapunov spectrum analytical instrument

摘要

PURPOSE: To allow expansion to a correlation dimension and a Lyapunov spectrum analysis of time-series data obtained from a nonautonomous system equation. CONSTITUTION: For data of time-series data Dx(t) (S1), a window process is performed which segments some time section out of the whole time-series data x(t), the nonautonomous system equation of the generation mechanism of the time-series data x(t) is approximated to an autonomous equation (S2), and an attracter is reconstituted by an embedding method for the time section (S3), and a correlation dimension is calculated for the reconstituted attracter (S4, S5, and S6), the steps (S2)-(S6) are repeated while the window of the time is gradually shifted with time, and a correlation dimension at each time is found.