Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent

Abstract

This study classified chaotic time series data, including smooth and nonsmooth problems in a dynamic system, using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. For this, the classical nonlinear differential equation by the Lorenz model was used to analyze a smooth dynamic system. The vibro-impact model was used for the nonsmooth dynamic system. Recurrence is a fundamental property of a dynamic system, and a recurrence plot is a representative method to visualize the recurrence characteristics of reconstructed phase space. Therefore, this study calculated the Lyapunov exponent by parametric analysis and visualized the corresponding recurrence matrix to show the dynamic characteristics as an image. In addition, the dynamic characteristics were classified using the proposed CNN model. The proposed CNN model determined chaos with an accuracy of more than 92%.