Deep learning-based classification of chaotic systems over phase portraits

Abstract

This study performed a deep learning-based classification of chaotic systems over their phase portraits. To the best of the authors’ knowledge, such classification studies over phase portraits have not been conducted in the literature. To that end, a dataset consisting of the phase portraits of the most known two chaotic systems, namely Lorenz and Chen, is generated for different values of the parameters, initial conditions, step size, and time length. Then, a classification with high accuracy is carried out employing transfer learning methods. The transfer learning methods used in the study are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet, and GoogLeNet deep learning models. As a result of the study, classification accuracy between 97.4% and 100% for 2-ways classifier and between 83.68% and 99.82% for 3-ways classifier is achieved depending on the problem. Thanks to this, random signals obtained in real life can be associated with a mathematical model.