Estimating the Time Delay of the Dynamical System Considering the Geometry of the Attractor

Abstract

In this paper, we propose a novel method for estimating the time delay in chaotic time series analysis. In recent years, focusing on the shape of an attractor using persistent homology has attracted attention. However, this method has a problem in that the calculation cost is enormous. In the proposed method, we aim to improve the calculation speed while considering the geometric shape of the attractor by focusing on the distance between the points in the data group.