Machine learning approach to detect dynamical states of nonlinear time series

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Using machine learning techniques, we classify various dynamical states underlying nonlinear time series data. We collect synthetic time series data by simulating standard dynamical models of Rössler, Lorenz, Chen, Duffing, 4D-Lorenz, 4D- Rössler systems. We use only single time series corresponding to the x-variable to reconstructed the system's trajectory or attractor in higher dimensions using Taken's embedding technique. Recurrence plots and recurrence networks are then constructed from the recurrence pattern of points on the reconstructed attractors. Further, we calculate recurrence measures from recurrence plots and average network properties from recurrence network. These measures are used as features for the machine learning models. We find all the supervised machine learning algorithms namely, logistic regression, random forest and support vector machine are effectively predicting series dynamical behavior and noisy patterns that emerges in nonlinear time series. However, if we assign rank, then Random Forest algorithm exhibits the highest accuracy followed by Support Vector Machine and then Logistic Regression. Our study indicates that among all the features we used, the features related to the density of the recurrence points or the closeness of points, such as recurrence rate, average path length, and trapping time, are the most effective in predicting the class of a given time series correctly. We also observe that even when the data has noise up to 5%⁠, the chaotic state of the time series, can be correctly identified using machine learning algorithms. Additionally, the trained algorithms are successfully applied to predict the dynamical states of two variable stars, SX Her and AC Her, from their light curve data.

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