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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Main Authors: Vasiliy Ye. Belozyorov, Dmytro M. Moroz, Svetlana A. Volkova
Format: Article
Language:English
Published: Oles Honchar Dnipro National University 2025-04-01
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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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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AT dmytrommoroz homoclinicandheteroclinicneuralodestheoryanditsusetoconstructnewchaoticattractors
AT svetlanaavolkova homoclinicandheteroclinicneuralodestheoryanditsusetoconstructnewchaoticattractors