Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors
New types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found. In the future, the implementation of these conditions guarantees the existence of chaotic att...
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2025-04-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/208 |
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| _version_ | 1849468862622334976 |
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| author | Vasiliy Ye. Belozyorov Dmytro M. Moroz Svetlana A. Volkova |
| author_facet | Vasiliy Ye. Belozyorov Dmytro M. Moroz Svetlana A. Volkova |
| author_sort | Vasiliy Ye. Belozyorov |
| collection | DOAJ |
| description | New types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found. In the future, the implementation of these conditions guarantees the existence of chaotic attractors in the mentioned NODE systems. |
| format | Article |
| id | doaj-art-5512ae56baa34d4a8ba40a7bb0b72ec0 |
| institution | Kabale University |
| issn | 2617-0108 2663-6824 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Journal of Optimization, Differential Equations and Their Applications |
| spelling | doaj-art-5512ae56baa34d4a8ba40a7bb0b72ec02025-08-20T03:25:43ZengOles Honchar Dnipro National UniversityJournal of Optimization, Differential Equations and Their Applications2617-01082663-68242025-04-01331154110.15421/142502200Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic AttractorsVasiliy Ye. Belozyorov0Dmytro M. Moroz1Svetlana A. Volkova2Department of Applied Mathematics, Oles Honchar Dnipro National UniversityDepartment of Computer Systems Software, National Technical University "Dnipro Polytechnic"Department of Computer Information Technologies, Ukrainian State University of Science and TechnologiesNew types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found. In the future, the implementation of these conditions guarantees the existence of chaotic attractors in the mentioned NODE systems.https://model-dnu.dp.ua/index.php/SM/article/view/208system of ordinary autonomous differential equationslimit cyclehomoclinic and heteroclinic orbitschaotic attractorneural network |
| spellingShingle | Vasiliy Ye. Belozyorov Dmytro M. Moroz Svetlana A. Volkova Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors Journal of Optimization, Differential Equations and Their Applications system of ordinary autonomous differential equations limit cycle homoclinic and heteroclinic orbits chaotic attractor neural network |
| title | Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors |
| title_full | Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors |
| title_fullStr | Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors |
| title_full_unstemmed | Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors |
| title_short | Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors |
| title_sort | homoclinic and heteroclinic neural odes theory and its use to construct new chaotic attractors |
| topic | system of ordinary autonomous differential equations limit cycle homoclinic and heteroclinic orbits chaotic attractor neural network |
| url | https://model-dnu.dp.ua/index.php/SM/article/view/208 |
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