The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks
Chaotic systems are nonlinear systems that show sensitive dependence on initial conditions, and an immeasurably small change in initial value causes an immeasurably large change in the future state of the system. Besides, there is no randomness in chaotic systems and they have an order within themse...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Akif AKGUL
2023-07-01
|
| Series: | Chaos Theory and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/2806626 |
| _version_ | 1797295294005641216 |
|---|---|
| author | Zeynep Keleş Güray Sonugür Murat Alçın |
| author_facet | Zeynep Keleş Güray Sonugür Murat Alçın |
| author_sort | Zeynep Keleş |
| collection | DOAJ |
| description | Chaotic systems are nonlinear systems that show sensitive dependence on initial conditions, and an immeasurably small change in initial value causes an immeasurably large change in the future state of the system. Besides, there is no randomness in chaotic systems and they have an order within themselves. Researchers use chaotic systems in many areas such as mixer systems that can make more homogeneous mixtures, encryption systems that can be used with high security, and artificial neural networks by taking the advantage of the order in this disorder. Differential equations in which chaotic systems are expressed mathematically are solved by numerical solution methods such as Heun, Euler, ODE45, RK4, RK5-Butcher and Dormand-Prince in the literature. In this research, Feed Forward Neural Network (FFNN), Layer Recurrent Neural Network (LRNN) and Cascade Forward Backpropogation Neural Network (CFNN) structures were used to model the Rucklidge chaotic system by making use of the MATLAB R2021A program Neural Network (NN) Toolbox. By comparing the results of different activation functions used in the modeling, the ANN structure that can best model the Rucklidge chaotic system has been determined. The training of the compared Artificial Neural Networks (ANNs) was carried out with the values obtained from the Euler numerical solution method, which can get satisfactory and fast results. |
| first_indexed | 2024-03-07T21:45:38Z |
| format | Article |
| id | doaj.art-acdb15a02c274d8bafb7bb0dac9338c8 |
| institution | Directory Open Access Journal |
| issn | 2687-4539 |
| language | English |
| last_indexed | 2024-03-07T21:45:38Z |
| publishDate | 2023-07-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj.art-acdb15a02c274d8bafb7bb0dac9338c82024-02-25T19:10:00ZengAkif AKGULChaos Theory and Applications2687-45392023-07-0152596410.51537/chaos.12130701971The Modeling of the Rucklidge Chaotic System with Artificial Neural NetworksZeynep Keleş0Güray Sonugür1Murat Alçın2AFYON KOCATEPE UNIVERSITYDept. of Mechatronic Engineering Faculty of Technology Afyon Kocatepe UniversityAFYON KOCATEPE UNIVERSITYChaotic systems are nonlinear systems that show sensitive dependence on initial conditions, and an immeasurably small change in initial value causes an immeasurably large change in the future state of the system. Besides, there is no randomness in chaotic systems and they have an order within themselves. Researchers use chaotic systems in many areas such as mixer systems that can make more homogeneous mixtures, encryption systems that can be used with high security, and artificial neural networks by taking the advantage of the order in this disorder. Differential equations in which chaotic systems are expressed mathematically are solved by numerical solution methods such as Heun, Euler, ODE45, RK4, RK5-Butcher and Dormand-Prince in the literature. In this research, Feed Forward Neural Network (FFNN), Layer Recurrent Neural Network (LRNN) and Cascade Forward Backpropogation Neural Network (CFNN) structures were used to model the Rucklidge chaotic system by making use of the MATLAB R2021A program Neural Network (NN) Toolbox. By comparing the results of different activation functions used in the modeling, the ANN structure that can best model the Rucklidge chaotic system has been determined. The training of the compared Artificial Neural Networks (ANNs) was carried out with the values obtained from the Euler numerical solution method, which can get satisfactory and fast results.https://dergipark.org.tr/en/download/article-file/2806626rucklidge chaotic systemeuler algorithmartificial neural networks |
| spellingShingle | Zeynep Keleş Güray Sonugür Murat Alçın The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks Chaos Theory and Applications rucklidge chaotic system euler algorithm artificial neural networks |
| title | The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks |
| title_full | The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks |
| title_fullStr | The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks |
| title_full_unstemmed | The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks |
| title_short | The Modeling of the Rucklidge Chaotic System with Artificial Neural Networks |
| title_sort | modeling of the rucklidge chaotic system with artificial neural networks |
| topic | rucklidge chaotic system euler algorithm artificial neural networks |
| url | https://dergipark.org.tr/en/download/article-file/2806626 |
| work_keys_str_mv | AT zeynepkeles themodelingoftherucklidgechaoticsystemwithartificialneuralnetworks AT guraysonugur themodelingoftherucklidgechaoticsystemwithartificialneuralnetworks AT muratalcın themodelingoftherucklidgechaoticsystemwithartificialneuralnetworks AT zeynepkeles modelingoftherucklidgechaoticsystemwithartificialneuralnetworks AT guraysonugur modelingoftherucklidgechaoticsystemwithartificialneuralnetworks AT muratalcın modelingoftherucklidgechaoticsystemwithartificialneuralnetworks |