Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures

Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures

We analyze dynamical systems of general form possessing gradient (symmetric) and Hamiltonian (antisymmetric) flow parts. The relevance of such systems to self-organizing processes is discussed. Coherent structure formation and related gradient flows on matrix Grassmann type manifolds are conside...

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Збережено в:
Бібліографічні деталі
Дата:2004
Автори: Gafiychuk, V.V., Prykarpatsky, A.K.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики конденсованих систем НАН України 2004
Назва видання:Condensed Matter Physics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/119026
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures / V.V. Gafiychuk, A.K. Prykarpatsky // Condensed Matter Physics. — 2004. — Т. 7, № 3(39). — С. 551–563. — Бібліогр.: 20 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1190262017-06-04T03:04:16Z Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures Gafiychuk, V.V. Prykarpatsky, A.K. We analyze dynamical systems of general form possessing gradient (symmetric) and Hamiltonian (antisymmetric) flow parts. The relevance of such systems to self-organizing processes is discussed. Coherent structure formation and related gradient flows on matrix Grassmann type manifolds are considered. The corresponding graph model associated with the partition swap neighborhood problem is studied. The criterion for emerging gradient and Hamiltonian flows is established. As an example we consider nonlinear dynamics in a neuron network system described by a simulative vector field. A simple criterion was written in order to establish conditions for the formation of an oscillatory pattern in a model neural system under consideration. Аналізуються динамічні системи загального виду, векторні поля яких складаються з градієнтної (симетричної) та Гамільтонової (антисиметричної) складових. Дискутується відповідність таких систем процесам самоорганізації. Розглядається виникнення когерентних структур і відповідних градієнтних потоків на грасманових многовидах, а також моделювання таких структур відповідною моделлю графа, який виникає в результаті такого формування. Встановлено критерій виникнення гамільтонових і градієнтних векторних полів. Розглядається модельний приклад нейронної динамічної системи, для якої встановлені умови виникнення осциляційних структур. 2004 Article Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures / V.V. Gafiychuk, A.K. Prykarpatsky // Condensed Matter Physics. — 2004. — Т. 7, № 3(39). — С. 551–563. — Бібліогр.: 20 назв. — англ. 1607-324X PACS: 05.45.-a, 07.05.Mh, 05.65.+b DOI:10.5488/CMP.7.3.551 http://dspace.nbuv.gov.ua/handle/123456789/119026 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We analyze dynamical systems of general form possessing gradient (symmetric) and Hamiltonian (antisymmetric) flow parts. The relevance of such systems to self-organizing processes is discussed. Coherent structure formation and related gradient flows on matrix Grassmann type manifolds are considered. The corresponding graph model associated with the partition swap neighborhood problem is studied. The criterion for emerging gradient and Hamiltonian flows is established. As an example we consider nonlinear dynamics in a neuron network system described by a simulative vector field. A simple criterion was written in order to establish conditions for the formation of an oscillatory pattern in a model neural system under consideration.
format Article
author Gafiychuk, V.V.
Prykarpatsky, A.K.
spellingShingle Gafiychuk, V.V.
Prykarpatsky, A.K.
Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
Condensed Matter Physics
author_facet Gafiychuk, V.V.
Prykarpatsky, A.K.
author_sort Gafiychuk, V.V.
title Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
title_short Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
title_full Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
title_fullStr Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
title_full_unstemmed Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures
title_sort pattern formation in neural dynamical systems governed by mutually hamiltonian and gradient vector field structures
publisher Інститут фізики конденсованих систем НАН України
publishDate 2004
url http://dspace.nbuv.gov.ua/handle/123456789/119026
citation_txt Pattern formation in neural dynamical systems governed by mutually Hamiltonian and gradient vector field structures / V.V. Gafiychuk, A.K. Prykarpatsky // Condensed Matter Physics. — 2004. — Т. 7, № 3(39). — С. 551–563. — Бібліогр.: 20 назв. — англ.
series Condensed Matter Physics
work_keys_str_mv AT gafiychukvv patternformationinneuraldynamicalsystemsgovernedbymutuallyhamiltonianandgradientvectorfieldstructures
AT prykarpatskyak patternformationinneuraldynamicalsystemsgovernedbymutuallyhamiltonianandgradientvectorfieldstructures
first_indexed 2023-10-18T20:33:37Z
last_indexed 2023-10-18T20:33:37Z
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