Topological Procedures for Finding Unstable Fixed Points from Time Series Data

Abstract

This study employs topological procedures to extract unstable fixed points in phase space from both numerical and experimental time series data. Conley index of an isolated invariant subset and the R-B method can determine unstable fixed points contained in strange attractor from numerical time series data. For experimental time series data, the theorem for the relationship between index pair and Conley index enables one to predict unstable fixed points with acceptable accuracy. Some examples for Duffing oscillator and piecewise linear system are shown.