Detection of deterministic and chaotic signals on the basis of the LSTM model training results.

Abstract

Detection of chaos in dynamical signals is an important and popular research area. Traditionally, the chaotic behavior is evaluated by calculating the Largest Lyapunov Exponent (LLE). However, calculating the LLE is sometimes difficult and requires specific data. Moreover, it introduces some subjective assumptions and is sometimes called a "manual" method. Therefore, there are many attempts to provide alternative ways to assess the dynamical signal as chaotic or deterministic. Some of them use deep learning methods. In this paper, we present a novel method of signal classification that is based on the assumption that it is easier to learn deterministic behavior than a chaotic one. We show that based on this assumption, it is possible to calculate the "amount of chaos" in the signal with the help of a simple LSTM (Long Short-Term Memory) neural network. The main advantage of this method is that-contrary to other deep learning-based methods-it does not require prior data to train the network as the results of the training process for a signal being classified are taken into account as the result of this evaluation. We confirm the method's validity using the publicly available dataset of chaotic and deterministic signals.