Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks
The study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4302505 |
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| _version_ | 1849304885192818688 |
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| author | Yusong Lu Ricai Luo Yongfu Zou |
| author_facet | Yusong Lu Ricai Luo Yongfu Zou |
| author_sort | Yusong Lu |
| collection | DOAJ |
| description | The study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure of Roslerʼs chaotic system. Furthermore, we analyzed the divergence, the eigenvalue of the Jacobian matrix for the equilibrium point, and the Lyapunov exponent of the system. These properties prove that the system does have chaotic behavior. This result not only confirms that there is chaos in the neural networks but also that the chaotic characteristics of the system are very similar to those of Roslerʼs chaotic system under certain conditions. This discovery provides useful information that can be applied to other aspects of chaotic Hopfield neural networks, such as chaotic synchronization and control. |
| format | Article |
| id | doaj-art-4036ce94c8bb409abd7f63c6cd318e5f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4036ce94c8bb409abd7f63c6cd318e5f2025-08-20T03:55:36ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/43025054302505Morphological Analysis for Three-Dimensional Chaotic Delay Neural NetworksYusong Lu0Ricai Luo1Yongfu Zou2Department of Mathematics and Statistics, Hechi University, Yizhou, ChinaDepartment of Mathematics and Statistics, Hechi University, Yizhou, ChinaDepartment of Mathematics and Statistics, Hechi University, Yizhou, ChinaThe study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure of Roslerʼs chaotic system. Furthermore, we analyzed the divergence, the eigenvalue of the Jacobian matrix for the equilibrium point, and the Lyapunov exponent of the system. These properties prove that the system does have chaotic behavior. This result not only confirms that there is chaos in the neural networks but also that the chaotic characteristics of the system are very similar to those of Roslerʼs chaotic system under certain conditions. This discovery provides useful information that can be applied to other aspects of chaotic Hopfield neural networks, such as chaotic synchronization and control.http://dx.doi.org/10.1155/2020/4302505 |
| spellingShingle | Yusong Lu Ricai Luo Yongfu Zou Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks Journal of Mathematics |
| title | Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks |
| title_full | Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks |
| title_fullStr | Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks |
| title_full_unstemmed | Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks |
| title_short | Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks |
| title_sort | morphological analysis for three dimensional chaotic delay neural networks |
| url | http://dx.doi.org/10.1155/2020/4302505 |
| work_keys_str_mv | AT yusonglu morphologicalanalysisforthreedimensionalchaoticdelayneuralnetworks AT ricailuo morphologicalanalysisforthreedimensionalchaoticdelayneuralnetworks AT yongfuzou morphologicalanalysisforthreedimensionalchaoticdelayneuralnetworks |