The Time Series Classification of Discrete-Time Chaotic Systems Using Deep Learning Approaches

Ömer Faruk Akmeşe, Berkay Emin, Yusuf Alaca, Yeliz Karaca () and Akif Akgül
Additional contact information
Ömer Faruk Akmeşe: Department of Computer Engineering, Faculty of Engineering, Hitit University, 19030 Çorum, Türkiye
Berkay Emin: Department of Electronics and Automation, Osmancık Omer Derindere Vocational School, Hitit University, 19500 Çorum, Türkiye
Yusuf Alaca: Department of Computer Engineering, Faculty of Engineering, Hitit University, 19030 Çorum, Türkiye
Yeliz Karaca: UMass Chan Medical School, University of Massachusetts, Worcester, MA 01655, USA
Akif Akgül: Department of Computer Engineering, Faculty of Engineering, Hitit University, 19030 Çorum, Türkiye

Mathematics, 2024, vol. 12, issue 19, 1-27

Abstract: Discrete-time chaotic systems exhibit nonlinear and unpredictable dynamic behavior, making them very difficult to classify. They have dynamic properties such as the stability of equilibrium points, symmetric behaviors, and a transition to chaos. This study aims to classify the time series images of discrete-time chaotic systems by integrating deep learning methods and classification algorithms. The most important innovation of this study is the use of a unique dataset created using the time series of discrete-time chaotic systems. In this context, a large and unique dataset representing various dynamic behaviors was created for nine discrete-time chaotic systems using different initial conditions, control parameters, and iteration numbers. The dataset was based on existing chaotic system solutions in the literature, but the classification of the images representing the different dynamic structures of these systems was much more complex than ordinary image datasets due to their nonlinear and unpredictable nature. Although there are studies in the literature on the classification of continuous-time chaotic systems, no studies have been found on the classification of discrete-time chaotic systems. The obtained time series images were classified with deep learning models such as DenseNet121, VGG16, VGG19, InceptionV3, MobileNetV2, and Xception. In addition, these models were integrated with classification algorithms such as XGBOOST, k-NN, SVM, and RF, providing a methodological innovation. As the best result, a 95.76% accuracy rate was obtained with the DenseNet121 model and XGBOOST algorithm. This study takes the use of deep learning methods with the graphical representations of chaotic time series to an advanced level and provides a powerful tool for the classification of these systems. In this respect, classifying the dynamic structures of chaotic systems offers an important innovation in adapting deep learning models to complex datasets. The findings are thought to provide new perspectives for future research and further advance deep learning and chaotic system studies.

Keywords: time series classification; chaotic systems; discrete-time chaotic systems; deep learning models; convolutional neural networks; classification algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3052/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3052/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3052-:d:1488593

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().