Recurrence quantification analysis and surrogate-based hypothesis testing for Rossler system with white noise

Abstract

Recurrence quantification analysis (RQA) and surrogate-based hypothesis testing are important tools in characterizing time series data. In this paper, we determine at what embedding dimensions the system becomes deterministic when a specific amount of noise is added to the Rossler system. We test the effectiveness of recurrence quantification analysis and surrogate-based hypothesis testing when dealing with synthetic data with added noise, specifically to determine if the RQA and surrogate-based hypothesis testing will recognize if the Rossler system is deterministic even at low added signal-to-noise (SNR). Our results show that at a low SNR (high added noise), the data is deterministic at higher embedding dimensions.