<p>This paper investigates the classification of conservative chaos and invariant tori in non-Hamiltonian conservative chaotic system, demonstrating how deep learning can efficiently handle large-scale data. Using the classical Sprott A system as a case study, we train three types of neural network models: Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Transformer to classify its time series. The results show that, compared with the traditional analytical method based on the Lyapunov exponents, deep learning methods can effectively reduce the computational time cost of classification while maintaining relatively high classification accuracy. This study not only confirms the effectiveness of deep learning for processing large-scale data but also offers a powerful tool for the global analysis of nonlinear dynamical systems.</p>

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Classifying conservative chaos and invariant tori by deep learning

  • Yue Li,
  • Yulong Shi,
  • Mingfeng Yuan,
  • Haopeng Wang,
  • Zengqiang Chen

摘要

This paper investigates the classification of conservative chaos and invariant tori in non-Hamiltonian conservative chaotic system, demonstrating how deep learning can efficiently handle large-scale data. Using the classical Sprott A system as a case study, we train three types of neural network models: Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Transformer to classify its time series. The results show that, compared with the traditional analytical method based on the Lyapunov exponents, deep learning methods can effectively reduce the computational time cost of classification while maintaining relatively high classification accuracy. This study not only confirms the effectiveness of deep learning for processing large-scale data but also offers a powerful tool for the global analysis of nonlinear dynamical systems.