Periodic Solutions to a Modified Elman Neural Network
Elman neural network is a recurrent neural network. Compared with traditional neural networks, an Elman neural network has additional inputs from the hidden layer, which form a new layer called the context layer. The standard back- propagation algorithm used in Elman neural networks is called back-p...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IFSA Publishing, S.L.
2021-04-01
|
| Series: | Sensors & Transducers |
| Subjects: | |
| Online Access: | https://sensorsportal.com/HTML/DIGEST/april_2021/Vol_251/P_3224.pdf |
| _version_ | 1797751336312242176 |
|---|---|
| author | Zlatinka KOVACHEVA Valéry COVACHEV |
| author_facet | Zlatinka KOVACHEVA Valéry COVACHEV |
| author_sort | Zlatinka KOVACHEVA |
| collection | DOAJ |
| description | Elman neural network is a recurrent neural network. Compared with traditional neural networks, an Elman neural network has additional inputs from the hidden layer, which form a new layer called the context layer. The standard back- propagation algorithm used in Elman neural networks is called back-propagation algorithm. Elman neural networks can be applied to solve prediction problems of discrete-time sequences. In the present paper, for a modified Elman neural network with a periodic input, we present sufficient conditions for the existence of a periodic output by using Mawhin’s continuation theorem of the coincidence degree theory. Examples are given of Elman neural networks satisfying these sufficient conditions. Periodic solutions are found for particular choices of the weights, self-feedback factor and periodic inputs. Further on, sufficient conditions are presented for the global asymptotic stability of a periodic output. The periodic outputs corresponding to the solutions previously found are shown to be globally asymptotically stable for any continuous transfer functions of the output layer. |
| first_indexed | 2024-03-12T16:45:57Z |
| format | Article |
| id | doaj.art-d301ad9fb23f4053bac87eb4f81a669e |
| institution | Directory Open Access Journal |
| issn | 2306-8515 1726-5479 |
| language | English |
| last_indexed | 2024-03-12T16:45:57Z |
| publishDate | 2021-04-01 |
| publisher | IFSA Publishing, S.L. |
| record_format | Article |
| series | Sensors & Transducers |
| spelling | doaj.art-d301ad9fb23f4053bac87eb4f81a669e2023-08-08T13:44:35ZengIFSA Publishing, S.L.Sensors & Transducers2306-85151726-54792021-04-0125144755Periodic Solutions to a Modified Elman Neural NetworkZlatinka KOVACHEVA0Valéry COVACHEV1Institute of Mathematics and Informatics, Bulgarian Academy of SciencesInstitute of Mathematics and Informatics, Bulgarian Academy of SciencesElman neural network is a recurrent neural network. Compared with traditional neural networks, an Elman neural network has additional inputs from the hidden layer, which form a new layer called the context layer. The standard back- propagation algorithm used in Elman neural networks is called back-propagation algorithm. Elman neural networks can be applied to solve prediction problems of discrete-time sequences. In the present paper, for a modified Elman neural network with a periodic input, we present sufficient conditions for the existence of a periodic output by using Mawhin’s continuation theorem of the coincidence degree theory. Examples are given of Elman neural networks satisfying these sufficient conditions. Periodic solutions are found for particular choices of the weights, self-feedback factor and periodic inputs. Further on, sufficient conditions are presented for the global asymptotic stability of a periodic output. The periodic outputs corresponding to the solutions previously found are shown to be globally asymptotically stable for any continuous transfer functions of the output layer.https://sensorsportal.com/HTML/DIGEST/april_2021/Vol_251/P_3224.pdfelman neural networkhidden layercontext layerperiodic input and outputmawhin’s continuation theoremglobal asymptotic stability |
| spellingShingle | Zlatinka KOVACHEVA Valéry COVACHEV Periodic Solutions to a Modified Elman Neural Network Sensors & Transducers elman neural network hidden layer context layer periodic input and output mawhin’s continuation theorem global asymptotic stability |
| title | Periodic Solutions to a Modified Elman Neural Network |
| title_full | Periodic Solutions to a Modified Elman Neural Network |
| title_fullStr | Periodic Solutions to a Modified Elman Neural Network |
| title_full_unstemmed | Periodic Solutions to a Modified Elman Neural Network |
| title_short | Periodic Solutions to a Modified Elman Neural Network |
| title_sort | periodic solutions to a modified elman neural network |
| topic | elman neural network hidden layer context layer periodic input and output mawhin’s continuation theorem global asymptotic stability |
| url | https://sensorsportal.com/HTML/DIGEST/april_2021/Vol_251/P_3224.pdf |
| work_keys_str_mv | AT zlatinkakovacheva periodicsolutionstoamodifiedelmanneuralnetwork AT valerycovachev periodicsolutionstoamodifiedelmanneuralnetwork |