Learning topological horseshoes in time series via deep neural networks.

Abstract

Time-series analysis plays a crucial role in understanding the dynamics of real-world systems across various scientific and engineering disciplines. We in this paper propose a novel approach to identifying chaotic dynamics by a geometric method based on deep learning. Specifically, we construct a map from the observed time-series data and seek the existence of a topological horseshoe in the map, which indicates chaotic behavior. We demonstrate the effectiveness of our method by numerical experiments on the Hénon map, the Lorenz system, and the Duffing system. The results show that the topological horseshoe theory combined with deep neural works provides a valuable tool for detection of chaos in complex nonlinear systems from time series.