Chaos Detection in Noisy Signals Using Refined Signal Representations

Discovering the characteristics of nonlinear dynamical systems is an important topic in many fields. When the governing equations are known, such analysis is straightforward; otherwise, as in the case of biological data, alternative approaches are required. This paper presents one such approach and is a continuation of previous studies on differentiating chaotic and non-chaotic behavior using machine learning and synthetic datasets generated from well-known dynamical systems. These datasets were used to extract refined representations, defined as groups of data with similar initial conditions. The method relies on phase-space reconstruction and data clustering. The refined representations were used for the classification of system dynamics using a Long Short-Term Memory (LSTM) network. The model was trained on both noise-free and noise-contaminated data and evaluated on noisy test sets from different dynamical systems. Results obtained for the refined representations were compared with those obtained for the original ones. The experiments showed that models trained on the refined representation generally achieved better classification performance, particularly under moderate-to-high noise conditions. However, this advantage was not consistent across all noise conditions, indicating that the effectiveness of the refined representation depends on both the type and the level of noise, as well as on the noise characteristics of the training data.