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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| Datum: | 2004 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики конденсованих систем НАН України
2004
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| Schriftenreihe: | Condensed Matter Physics |
| Online Zugang: | 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 |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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. |
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